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[(can)-318(reveal)-318(hidden)-318(risks)-318(of)-318(public)-318(health)-318(decisions.)]TJ 0.005 Tc 1 -1.088 Td [(To)-278(de)20(scribe)-278(the)-278(dynamics)-278(of)-278(smallpox,)-278(we)-278(use)-278(the)-278(well)-278(k)-30(nown)]TJ -1 -1.088 Td [(susceptible-ex)-30(posed-infected-removed)-338(\(SEIR\))-338(model)-338(\(2\):)]TJ /T1_6 1 Tf 0.0199 Tc 10.353 -1.966 Td (dS)Tj ET 0 0 0 1 K 0.25 w 10 M 0 j 0 J []0 d 144.849 165.918 m 154.898 165.918 l S BT /T1_6 1 Tf 9 0 0 9 146.0682 156.9943 Tm (dt)Tj /T1_7 1 Tf 0 Tc 1.203 0.63 Td (\001)Tj /T1_3 1 Tf 1.075 0.812 Td (\002)Tj /T1_6 1 Tf 0.853 0 Td (R)Tj /T1_5 1 Tf 6.3977 0 0 5.7614 181.05 168.3807 Tm (0)Tj /T1_7 1 Tf 9 0 1.3977 9 184.4591 169.9716 Tm (\002)Tj ET 166.568 165.918 m 190.219 165.918 l S BT /T1_6 1 Tf 9 0 0 9 174.6591 156.9943 Tm (N)Tj 0.0849 Tc 2.064 0.63 Td (SI)Tj /T1_5 1 Tf 0 Tc 1.084 0 Td (,)Tj /T1_6 1 Tf 0.0199 Tc -6.588 -2.6 Td (dE)Tj ET 143.696 135.213 m 154.886 135.213 l S BT /T1_6 1 Tf 9 0 0 9 145.4858 126.2898 Tm (dt)Tj /T1_7 1 Tf 0 Tc 1.267 0.63 Td (\001)Tj /T1_6 1 Tf 1.075 0.812 Td (R)Tj /T1_5 1 Tf 6.3977 0 0 5.7614 172.7778 137.6761 Tm (0)Tj /T1_7 1 Tf 9 0 1.3977 9 176.1044 139.267 Tm (\002)Tj ET 166.557 135.213 m 181.281 135.213 l S BT /T1_6 1 Tf 9 0 0 9 170.4773 126.2898 Tm (N)Tj 0.0199 Tc 1.47 0.63 Td (SI)Tj /T1_7 1 Tf 0 Tc 1.176 0 Td (\003)Tj 9 0 1.3977 9 203.964 131.963 Tm (\004)Tj /T1_6 1 Tf 9 0 0 9 209.6418 131.963 Tm (E)Tj /T1_5 1 Tf 0.696 0 Td (,)Tj /T1_6 1 Tf 0.0199 Tc -7.712 -2.6 Td (dI)Tj ET 146.494 104.509 m 154.886 104.509 l S BT /T1_6 1 Tf 9 0 0 9 146.8864 95.5852 Tm (dt)Tj /T1_7 1 Tf 0 Tc 1.111 0.63 Td (\001)Tj 9 0 1.3977 9 166.56 101.2585 Tm (\004)Tj /T1_6 1 Tf 9 0 0 9 172.2378 101.2585 Tm (E)Tj /T1_7 1 Tf 0.918 0 Td (\003)Tj 9 0 1.3977 9 190.1705 101.2585 Tm (\002)Tj /T1_6 1 Tf 9 0 0 9 195.3533 101.2585 Tm (I)Tj /T1_5 1 Tf 0.385 0 Td (,)Tj /T1_8 1 Tf 0.0199 Tc 9.73 1.778 Td ([1])Tj /T1_6 1 Tf -15.85 -4.378 Td (dR)Tj ET 143.741 73.804 m 154.886 73.804 l S BT /T1_6 1 Tf 9 0 0 9 145.5085 64.8807 Tm (dt)Tj /T1_7 1 Tf 0 Tc 1.264 0.63 Td (\001)Tj 9 0 1.3977 9 166.56 70.554 Tm (\002)Tj /T1_6 1 Tf 9 0 0 9 171.7428 70.554 Tm (I)Tj /T1_5 1 Tf 0.385 0 Td (.)Tj /T1_6 1 Tf 15.441 57.926 Td (R)Tj /T1_5 1 Tf 6.5 0 0 6 320.0814 590.6335 Tm (0)Tj -0.0149 Tc 9 0 0 9 327.2747 591.8835 Tm [(is)-449(the)-449(number)-449(of)-449(sec)-30(ondar)-60(y)-449(infections)-449(produced)-449(by)-449(a)-449(single)]TJ -1.455 -1.115 Td [(infected)-363(indiv)-40(idual,)]TJ /T1_7 1 Tf 0 Tc 9 0 1.3977 9 389.9017 581.8495 Tm (\002)Tj /T1_5 1 Tf -0.0149 Tc 9 0 0 9 398.0362 581.8495 Tm [(is)-363(the)-363(rate)-363(at)-363(which)-363(infectious)-363(indiv)-40(iduals)]TJ /T1_6 1 Tf 0 Tc 17.825 0 Td (I)Tj /T1_5 1 Tf -0.0149 Tc -27.143 -1.115 Td [(cease)-333(to)-333(be)-333(infectious)-333(because)-333(of)-333(rec)-30(over)-60(y)-333(or)-333(death,)-333(and)]TJ /T1_6 1 Tf 0 Tc 24.145 0 Td (N)Tj /T1_5 1 Tf -0.0149 Tc 1.063 0 Td [(is)-333(the)]TJ -25.208 -1.115 Td [(population)-263(size,)-263(here)-263(assumed)-263(to)-263(be)-263(of)-263(a)-263(single)-263(cit)-30(y.)-263(Hosts)-263(begin)-263(in)]TJ 0 -1.115 TD [(the)-178(un)-30(infected,)-178(non)-30(immune)-178(class)]TJ /T1_6 1 Tf 0 Tc 13.637 0 Td (S)Tj /T1_5 1 Tf -0.0149 Tc 0.712 0 Td [(and)-178(move)-178(to)-178(the)-178(ex)-30(posed)-178(but)-178(not)]TJ -14.349 -1.115 Td [(yet)-267(infectious)-267(class)]TJ /T1_6 1 Tf 0 Tc 7.927 0 Td (E)Tj /T1_5 1 Tf 0.2522 Tc 0.928 0 Td [(a)267(tar)267(a)267(t)267(e)]TJ /T1_6 1 Tf 0 Tc 3.705 0 Td (R)Tj /T1_5 1 Tf 6.5 0 0 6 433.1226 540.4631 Tm (0)Tj /T1_7 1 Tf 9 0 1.3977 9 436.279 541.7131 Tm (\002)Tj /T1_5 1 Tf -0.0149 Tc 9 0 0 9 443.5527 541.7131 Tm [(.)-267(Ex)-30(posed)-267(but)-267(not)-267(yet)-267(infectious)]TJ -14.375 -1.115 Td [(indiv)-40(iduals)-287(move)-287(to)-287(the)-287(infectious)-287(class)-287(at)-287(rate)]TJ /T1_7 1 Tf 0 Tc 9 0 1.3977 9 489.9526 531.679 Tm (\004)Tj /T1_5 1 Tf -0.0149 Tc 9 0 0 9 495.3179 531.679 Tm [(.)-287(To)-287(fit)-287(the)-287(model)]TJ -20.127 -1.115 Td [(to)-295(mort)-30(alit)-30(y)-295(dat)-30(a,)-295(we)-295(also)-295(introduce)-295(the)-295(parameter)]TJ /T1_7 1 Tf 0 Tc 9 0 1.3977 9 507.1794 521.6449 Tm (\005)Tj /T1_5 1 Tf -0.0149 Tc 9 0 0 9 513.0487 521.6449 Tm [(,)-295(the)-295(f)-30(raction)]TJ -22.097 -1.115 Td [(of)-318(removed)-318(indiv)-40(iduals)-318(that)-318(die)-318(of)-318(the)-318(disease.)]TJ 0.005 Tc 1 -1.115 Td [(The)-429(SEIR)-429(model)-429(has)-429(several)-429(useful)-429(feature)20(s)-429(for)-429(e)20(stimating)]TJ -1 -1.115 Td [(uncert)-30(aint)-30(y)-212(in)-212(the)-212(predictions)-212(of)-212(epidemic)-212(models.)-212(First,)-212(because)]TJ T* [(the)-309(model)-309(is)-309(based)-309(on)-309(assumptions)-309(that)-309(are)-309(approx)-50(imately)-309(tr)-30(ue)]TJ 0 -1.115 TD [(for)-434(many)-434(disease)20(s)-434(\(2\),)-434(it)-434(can)-434(be)-434(used)-434(for)-434(disease)20(s)-434(other)-434(than)]TJ T* [(smallpox)-270(\(7,)-270(9,)-270(10\),)-270(emphasizing)-270(the)-270(generalit)-30(y)-270(of)-270(our)-270(approach.)]TJ T* [(Sec)-30(ond,)-326(although)-326(the)-326(SEIR)-326(model)-326(has)-326(only)-326(four)-326(parameters,)-326(it)]TJ T* [(prov)-40(ide)20(s)-253(a)-253(good)-252(fit)-253(to)-253(dat)-30(a)-253(for)-253(historical)-253(smallpox)-253(epidemics)-253(\(3\).)]TJ T* [(The)-360(number)-360(of)-360(parameters)-360(in)-360(our)-360(model)-360(is)-360(import)-30(ant)-360(because)]TJ T* [(c)-30(oncerns)-477(over)-477(the)-477(c)-30(omplex)-50(it)-30(y)-477(of)-477(disease)-477(spread)-477(have)-477(caused)]TJ T* [(some)-243(re)20(searchers)-243(to)-243(instead)-243(c)-30(onstr)-30(uct)-243(c)-30(omplex)-243(models)-243(w)-40(ith)-243(tens)]TJ T* [(to)-187(hundreds)-187(of)-187(parameters)-187(\(4)-90(\226)-90(6\).)-187(Estimating)-187(the)-187(value)20(s)-187(of)-187(a)-187(large)]TJ T* [(number)-193(of)-193(parameters,)-193(however,)-193(require)20(s)-193(a)-193(large)-193(amount)-193(of)-193(dat)-30(a,)]TJ 0 -1.114 TD [(mak)-30(ing)-196(it)-196(impractical)-196(to)-196(for)-30(mally)-196(quantif)-30(y)-196(parameter)-196(uncert)-30(aint)-30(y)]TJ T* [(for)-607(c)-30(omplex)-607(models.)-607(Because)-607(the)-607(SEIR)-607(model)-607(in)-607(c)-30(ontrast)]TJ 0 -1.114 TD [(include)20(s)-212(only)-212(four)-212(parameters,)-212(e)20(stimating)-212(the)-212(overall)-212(uncert)-30(aint)-30(y)]TJ 0 -1.114 TD [(in)-332(its)-332(parameters)-332(is)-332(relatively)-332(straightfor)-30(ward.)-332(Moreover,)-332(as)-332(we)]TJ T* [(discuss)-301(further)-301(below,)-301(uncert)-30(aint)-30(y)-301(in)-301(model)-301(predictions)-301(is)-301(likely)]TJ T* [(to)-338(be)-338(even)-338(higher)-338(for)-338(models)-338(w)-40(ith)-338(many)-338(parameters.)]TJ -0.0149 Tc 1 -1.114 Td [(A)-522(c)-30(ommon)-522(method)-522(of)-522(quantif)-30(ying)-522(the)-522(ef)-30(fects)-522(of)-522(parameter)]TJ -1 -1.114 Td [(uncert)-30(aint)-30(y)-436(on)-436(the)-436(predictions)-436(of)-436(epidemic)-436(models)-436(is)-436(sensitiv)-40(it)-30(y)]TJ T* [(analysis,)-276(in)-276(which)-276(one)-276(or)-276(a)-276(few)-276(parameters)-276(are)-276(varied,)-276(whereas)-276(the)]TJ T* [(others)-584(are)-584(held)-584(c)-30(onst)-30(ant)-584(\(4,)-584(6\).)-584(Sensitiv)-40(it)-30(y)-584(analysis,)-584(however,)]TJ T* [(generally)-245(undere)20(stimate)20(s)-245(overall)-245(parameter)-245(uncert)-30(aint)-30(y.)-245(We)-245(there-)]TJ T* [(fore)-277(instead)-277(use)-277(Baye)20(s\222)-277(Theorem,)-277(which)-277(allows)-277(us)-277(to)-277(for)-30(mally)-277(t)-30(ake)]TJ T* [(into)-367(ac)-30(c)-30(ount)-367(uncert)-30(aint)-30(y)-367(in)-367(all)-367(parameters)-367(\(see)-367(supporting)-367(infor-)]TJ T* [(mation,)-318(which)-318(is)-318(published)-318(on)-318(the)-318(PNAS)-318(web)-318(site\):)]TJ /T1_6 1 Tf 0 Tc 0 -1.992 TD (P)Tj /T1_3 1 Tf 0.62 0 Td (\003)Tj /T1_6 1 Tf 0.353 0 Td (R)Tj /T1_5 1 Tf 6.3977 0 0 5.7614 329.1485 231.3693 Tm (0)Tj 9 0 0 9 332.4752 232.9602 Tm (,)Tj /T1_7 1 Tf 9 0 1.3977 9 337.333 232.9602 Tm (\004)Tj /T1_5 1 Tf 9 0 0 9 343.0108 232.9602 Tm (,)Tj /T1_7 1 Tf 9 0 1.3977 9 347.8687 232.9602 Tm (\002)Tj /T1_5 1 Tf 9 0 0 9 353.0514 232.9602 Tm (,)Tj /T1_7 1 Tf 9 0 1.3977 9 357.9093 232.9602 Tm (\005)Tj /T1_5 1 Tf 9 0 0 9 364.091 232.9602 Tm (,)Tj /T1_7 1 Tf 9 0 1.3977 9 368.9489 232.9602 Tm (\006)Tj /T1_5 1 Tf 6.3977 0 0 5.7614 374.6266 236.5398 Tm (2)Tj /T1_4 1 Tf 9 0 0 9 377.9533 232.9602 Tm (\001)Tj /T1_5 1 Tf 0.0199 Tc 0.242 0 Td [(dat)-30(a)]TJ /T1_3 1 Tf 0 Tc 1.969 0 Td (\004)Tj -8.455 -1.995 Td (\005)Tj /T1_7 1 Tf 9 0 1.3977 9 331.534 215.0057 Tm (\007)Tj /T1_3 1 Tf 9 0 0 9 338.301 215.0057 Tm (\003)Tj /T1_6 1 Tf 0.418 0 Td (R)Tj /T1_5 1 Tf 6.3977 0 0 5.7614 348.865 213.4148 Tm (0)Tj /T1_3 1 Tf 9 0 0 9 352.2741 215.0057 Tm (\004)Tj /T1_7 1 Tf 9 0 1.3977 9 356.0352 215.0057 Tm (\007)Tj /T1_3 1 Tf 9 0 0 9 362.8022 215.0057 Tm (\003)Tj /T1_7 1 Tf 9 0 1.3977 9 366.5632 215.0057 Tm (\004)Tj /T1_3 1 Tf 9 0 0 9 372.8262 215.0057 Tm (\004)Tj /T1_7 1 Tf 9 0 1.3977 9 376.5873 215.0057 Tm (\007)Tj /T1_3 1 Tf 9 0 0 9 383.3542 215.0057 Tm (\003)Tj /T1_7 1 Tf 9 0 1.3977 9 387.1153 215.0057 Tm (\002)Tj /T1_3 1 Tf 9 0 0 9 392.8833 215.0057 Tm (\004)Tj /T1_7 1 Tf 9 0 1.3977 9 396.6444 215.0057 Tm (\007)Tj /T1_3 1 Tf 9 0 0 9 403.4114 215.0057 Tm (\003)Tj /T1_7 1 Tf 9 0 1.3977 9 407.1724 215.0057 Tm (\005)Tj /T1_3 1 Tf 9 0 0 9 413.9394 215.0057 Tm (\004)Tj /T1_7 1 Tf 9 0 1.3977 9 417.7005 215.0057 Tm (\007)Tj /T1_3 1 Tf 9 0 0 9 424.4674 215.0057 Tm (\003)Tj /T1_7 1 Tf 9 0 1.3977 9 428.2285 215.0057 Tm (\006)Tj /T1_5 1 Tf 6.3977 0 0 5.7614 434.4915 218.5852 Tm (2)Tj /T1_3 1 Tf 9 0 0 9 437.9006 215.0057 Tm (\004)Tj /T1_9 1 Tf 0.418 0 Td (L)Tj /T1_3 1 Tf 0.535 0 Td (\003)Tj /T1_5 1 Tf 0.005 Tc 0.418 0 Td [(dat)-30(a)]TJ /T1_4 1 Tf 0 Tc 1.909 0 Td (\001)Tj /T1_6 1 Tf 0.307 0 Td (R)Tj /T1_5 1 Tf 6.3977 0 0 5.7614 476.9851 213.4148 Tm (0)Tj 9 0 0 9 480.3942 215.0057 Tm (,)Tj /T1_7 1 Tf 9 0 1.3977 9 486.4225 215.0057 Tm (\004)Tj /T1_5 1 Tf 9 0 0 9 492.6855 215.0057 Tm (,)Tj /T1_7 1 Tf 9 0 1.3977 9 498.7138 215.0057 Tm (\002)Tj /T1_5 1 Tf 9 0 0 9 504.4819 215.0057 Tm (,)Tj /T1_7 1 Tf 9 0 1.3977 9 510.5102 215.0057 Tm (\005)Tj /T1_5 1 Tf 9 0 0 9 517.2771 215.0057 Tm (,)Tj /T1_7 1 Tf 9 0 1.3977 9 523.3054 215.0057 Tm (\006)Tj /T1_5 1 Tf 6.3977 0 0 5.7614 529.5684 218.5852 Tm (2)Tj /T1_3 1 Tf 9 0 0 9 532.9775 215.0057 Tm (\004)Tj /T1_5 1 Tf 0.418 0 Td (.)Tj /T1_8 1 Tf 0.0199 Tc 1.355 0 Td ([2])Tj /T1_5 1 Tf 0.005 Tc -26.084 -2.006 Td (Here,)Tj /T1_7 1 Tf 0 Tc 9 0 1.3977 9 340.1154 196.9517 Tm (\006)Tj /T1_5 1 Tf 6.5 0 0 6 345.6596 199.9517 Tm (2)Tj 0.005 Tc 9 0 0 9 352.6938 196.9517 Tm [(repre)20(sents)-417(the)-417(random)-417(variation)-417(in)-417(the)-417(dat)-30(a)-417(beyond)]TJ -4.28 -1.114 Td [(what)-192(can)-192(be)-192(ex)-30(plained)-192(by)-192(the)-192(SEIR)-192(model.)-192(The)-192(uncert)-30(aint)-30(y)-192(in)-192(the)]TJ 0 -1.114 TD [(model\222s)-456(parameters)-456(then)-456(is)-456(repre)20(sented)-456(by)-456(the)-456(spread)-456(in)-456(the)]TJ T* [(posterior)-272(distribution)-272(of)-272(the)-272(parameters)-272(given)-272(the)-272(dat)-30(a,)]TJ /T1_6 1 Tf 0 Tc 24.08 0 Td (P)Tj /T1_5 1 Tf 0.605 0 Td (\()Tj /T1_6 1 Tf 0.388 0 Td (R)Tj /T1_5 1 Tf 6.5 0 0 6 545.9164 165.6335 Tm (0)Tj 9 0 0 9 549.1978 166.8835 Tm (,)Tj /T1_7 1 Tf 9 0 1.3977 9 553.9391 166.8835 Tm (\004)Tj /T1_5 1 Tf 9 0 0 9 559.4834 166.8835 Tm (,)Tj ET 314.176 151.509 m 386.176 151.509 l S BT /T1_2 1 Tf 6 0 0 6 314.1761 138.8835 Tm [(Author)-387(contributions:)-387(B.D.E.)-387(and)-387(G.D.)-387(designed)-387(research;)-387(B.D.E.)-387(and)-387(V.M.D.)-387(performed)]TJ 0 -1.333 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[(c)-30(onstr)-30(ucted)-396(priors)-396(for)-396(the)-396(parameters)-396(f)-30(rom)-396(literature)-396(dat)-30(a)-396(on)]TJ 0 -1.16 TD [(smallpox)-530(prog)-20(re)20(ssion)-530(\()]TJ /T1_3 1 Tf 10.289 0 Td (Methods)Tj /T1_1 1 Tf 4.106 0 Td [(and)-530(supporting)-530(infor)-30(mation\).)]TJ -14.395 -1.16 Td [(Sec)-30(ond,)-442(we)-442(calculated)-442(the)-442(likelihood)-442(of)-442(the)-442(parameters)-442(f)-30(rom)]TJ T* [(dat)-30(a)-232(on)-232(13)-232(past)-232(smallpox)-232(epidemics)-232(\(listed)-232(in)-232(Table)-232(3\).)-232(Third,)-232(we)]TJ T* [(c)-30(ombined)-435(the)-435(likelihood)-435(and)-435(the)-435(priors)-435(to)-435(calculate)-435(the)-435(joint)]TJ 0 -1.159 TD [(posterior)-468(distribution)-468(of)-468(the)-468(parameters,)-468(ac)-30(c)-30(ording)-468(to)-468(Baye)20(s\222)]TJ T* [(Theorem,)-356(Eq.)]TJ /T1_4 1 Tf 0 Tc 6.449 0 Td (2)Tj /T1_1 1 Tf 0.005 Tc 0.505 0 Td [(.)-356(We)-356(thus)-356(allowed)-356(for)-356(uncert)-30(aint)-30(y)-356(in)-356(all)-356(model)]TJ -6.954 -1.159 Td [(parameters,)-453(and)-453(we)-453(c)-30(ombined)-453(infor)-30(mation)-453(f)-30(rom)-453(all)-453(available)]TJ T* [(dat)-30(a.)-312(A)-30(lthough)-312(alternative)-312(approache)20(s)-312(also)-312(might)-312(have)-312(allowed)]TJ T* [(us)-282(to)-282(c)-30(ombine)-282(dat)-30(a,)-282(such)-282(approache)20(s)-282(are)-282(generally)-282(le)20(ss)-282(ef)-30(ficient)]TJ T* [(\(see)-411(supporting)-411(infor)-30(mation\).)-411(Similarly,)-411(although)-411(prev)-40(ious)-411(re-)]TJ T* [(searchers)-214(also)-214(have)-214(used)-214(multiple)-214(dat)-30(a)-214(sets,)-214(in)-214(so)-214(doing)-214(they)-214(have)]TJ 0 -1.159 TD [(assumed)-352(that)-352(the)-352(uncert)-30(aint)-30(y)-352(in)-352(some)-352(\(5,)-352(7,)-352(8,)-352(11\))-352(or)-352(all)-352(\(3,)-352(9\))]TJ T* [(other)-252(parameters)-252(is)-252(zero.)-252(As)-252(we)-252(w)-40(ill)-252(show,)-252(this)-252(assumption)-252(leads)]TJ T* [(to)-483(serious)-483(undere)20(stimate)20(s)-483(of)-483(parameter)-483(uncert)-30(aint)-30(y.)-483(A)-30(lso,)-483(in)]TJ T* [(e)20(stimating)-300(a)-300(single)-300(value)-300(of)]TJ /T1_3 1 Tf 0 Tc 12.111 0 Td (R)Tj /T1_1 1 Tf 6.5 0 0 6 166.7617 261.8381 Tm (0)Tj 0.005 Tc 9 0 0 9 172.742 263.0881 Tm [(f)-30(rom)-300(multiple)-300(epidemics,)-300(we)-300(are)]TJ -13.452 -1.159 Td [(ef)-30(fectively)-467(assuming)-467(that)-467(c)-30(ont)-30(act)-467(net)-30(works)-467(were)-467(the)-467(same)-467(in)]TJ 0 -1.159 TD [(dif)-30(ferent)-286(populations.)-286(A)-30(lthough)-286(this)-286(assumption)-286(is)-286(undoubtedly)]TJ T* [(unrealistic,)-453(allow)-40(ing)-453(for)-453(population-specific)-453(value)20(s)-453(of)]TJ /T1_3 1 Tf 0 Tc 24.164 0 Td (R)Tj /T1_1 1 Tf 6.5 0 0 6 275.2405 230.5426 Tm (0)Tj 0.005 Tc 9 0 0 9 282.5957 231.7926 Tm [(ver)-60(y)]TJ -25.658 -1.159 Td [(likely)-370(would)-370(lead)-370(to)-370(even)-370(more)-370(uncert)-30(aint)-30(y)-370(in)-370(the)-370(parameters.)]TJ T* [(Because)-388(our)-388(intent)-388(is)-388(to)-388(demonstrate)-388(that)-388(uncert)-30(aint)-30(y)-388(is)-388(high,)]TJ T* [(assuming)-338(a)-338(c)-30(ommon)-338(value)-338(of)]TJ /T1_3 1 Tf 0 Tc 13.112 0 Td (R)Tj /T1_1 1 Tf 6.5 0 0 6 175.772 199.2472 Tm (0)Tj 0.005 Tc 9 0 0 9 182.0931 200.4972 Tm [(thus)-338(is)-338(c)-30(onser)-60(vative.)]TJ -13.491 -1.159 Td [(To)-470(show)-470(how)-470(uncert)-30(aint)-30(y)-470(in)-470(parameter)-470(value)20(s)-470(can)-470(lead)-470(to)]TJ -1 -1.159 Td [(uncert)-30(aint)-30(y)-254(in)-254(evaluations)-254(of)-254(public)-254(health)-254(re)20(sponse)20(s)-254(to)-254(epidem-)]TJ T* [(ics,)-295(we)-295(translated)-295(parameter)-295(uncert)-30(aint)-30(y)-295(into)-295(uncert)-30(aint)-30(y)-295(in)-295(the)]TJ T* [(relative)-411(ef)-30(ficienc)-30(y)-411(of)-411(t)-30(wo)-411(dif)-30(ferent)-411(vac)-30(cination)-411(strategie)20(s.)-411(The)]TJ 0 -1.159 TD [(t)-30(wo)-526(strategie)20(s)-526(are)-526(mass)-526(vac)-30(cination,)-526(under)-526(which)-526(the)-526(entire)]TJ T* [(population)-336(is)-336(vac)-30(cinated)-336(at)-336(the)-336(beginn)-30(ing)-336(of)-336(the)-336(epidemic,)-336(and)]TJ T* [(trace)-430(vac)-30(cination,)-430(under)-430(which)-430(vac)-30(cinations)-430(are)-430(given)-430(only)-430(to)]TJ T* [(those)-284(who)-284(c)-30(ont)-30(act)-284(infected)-284(indiv)-40(iduals.)-284(A)-30(lthough)-284(mass)-284(vac)-30(cina-)]TJ T* [(tion)-194(is)-194(the)-194(polic)-30(y)-194(of)-194(the)-194(U.S.)-194(and)-194(U.K.)-194(governments)-194(\(12,)-194(13\),)-194(trace)]TJ T* [(vac)-30(cination)-301(was)-301(used)-301(in)-301(the)-301(final)-301(st)-30(age)20(s)-301(of)-301(smallpox)-301(eradication)]TJ T* [(\(12,)-286(14\))-286(and,)-286(recently,)-286(some)-286(re)20(searchers)-286(have)-286(argued)-286(that)-286(it)-286(w)-40(ill)]TJ T* [(be)-566(as)-566(ef)-30(fective)-566(as)-566(mass)-566(vac)-30(cination)-566(while,)-566(of)-566(c)-30(ourse,)-566(being)]TJ T* [(cheaper)-224(\(4,)-224(5\).)-224(The)20(se)-224(t)-30(wo)-224(strategie)20(s)-224(are)-224(not)-224(the)-224(only)-224(possibilitie)20(s,)]TJ 29.167 44.056 Td [(but)-272(they)-272(allow)-272(us)-272(to)-272(clearly)-272(show)-272(how)-272(uncert)-30(aint)-30(y)-272(in)-272(parameters)]TJ 0 -1.131 TD [(is)-338(translated)-338(into)-338(uncert)-30(aint)-30(y)-338(in)-338(strateg)-40(y)-338(evaluations.)]TJ 1 -1.131 Td [(The)-259(particular)-259(vac)-30(cination)-259(model)-259(that)-259(we)-259(used)-259(was)-259(developed)]TJ -1 -1.13 Td [(by)-247(Kaplan)]TJ /T1_3 1 Tf 4.605 0 Td [(et)-247(al)-30(.)]TJ /T1_1 1 Tf 2.272 0 Td [(\(11\).)-247(For)-247(our)-247(purpose)20(s,)-247(this)-247(model)-247(is)-247(c)-30(onven)-30(ient)]TJ -6.877 -1.13 Td [(because)-415(it)-415(is)-415(e)20(ssentially)-415(the)-415(SEIR)-415(model)-415(w)-40(ith)-415(the)-415(addition)-415(of)]TJ 0 -1.13 TD [(either)-286(mass)-286(or)-286(trace)-286(vac)-30(cination)-286(\(see)]TJ /T1_3 1 Tf 16.154 0 Td [(Suppor)-30(ting)-286(Te)-30(x)-30(t)]TJ /T1_1 1 Tf 6.949 0 Td [(for)-286(det)-30(ails)]TJ -23.103 -1.13 Td [(of)-339(the)-339(Kaplan)]TJ /T1_3 1 Tf 6.405 0 Td [(et)-339(al)-30(.)]TJ /T1_1 1 Tf 2.455 0 Td [(model\).)-339(The)-339(Kaplan)]TJ /T1_3 1 Tf 9.202 0 Td [(et)-339(al)-30(.)]TJ /T1_1 1 Tf 2.455 0 Td [(\(11\))-339(model)-339(thus)]TJ -20.516 -1.13 Td [(inherits)-426(assumptions)-426(of)-426(the)-426(SEIR)-426(model,)-426(such)-426(as)-426(ex)-30(ponential)]TJ 0 -1.13 TD [(sojourn)-385(time)20(s)-385(in)-385(each)-385(st)-30(age)-385(and)-385(homogeneous)-385(mix)-50(ing)-385(of)-385(indi-)]TJ T* [(v)-40(iduals,)-326(that)-326(are)-326(not)-326(nece)20(ssarily)-326(realistic.)-326(We)-326(therefore)-326(empha-)]TJ T* [(size)-286(that)-286(we)-286(use)-286(this)-286(model)-286(not)-286(because)-286(it)-286(is)-286(nece)20(ssarily)-286(the)-286(be)20(st)]TJ T* [(model,)-613(but)-613(because)-613(our)-613(aim)-613(is)-613(to)-613(illustrate)-613(the)-613(ef)-30(fects)-613(of)]TJ 0 -1.13 TD [(parameter)-372(uncert)-30(aint)-30(y)-372(on)-372(evaluations)-372(of)-372(vac)-30(cination)-372(strategie)20(s)]TJ T* [(rather)-440(than)-440(to)-440(identif)-30(y)-440(the)-440(be)20(st)-440(of)-440(all)-440(possible)-440(strategie)20(s.)-440(We)]TJ T* [(therefore)-432(c)-30(ompared)-432(the)-432(t)-30(wo)-432(vac)-30(cination)-432(strategie)20(s)-432(in)-432(the)-432(fol-)]TJ T* [(low)-40(ing)-303(way.)-303(First,)-303(we)-303(drew)-303(a)-303(large)-303(number)-303(of)-303(sets)-303(of)-303(parameter)]TJ T* [(value)20(s)-325(f)-30(rom)-325(the)-325(posterior)-325(distribution)-325(of)-325(the)-325(SEIR)-325(parameters.)]TJ T* [(Sec)-30(ond,)-392(we)-392(used)-392(each)-392(set)-392(of)-392(parameters)-392(in)-392(simulations)-392(of)-392(the)]TJ T* (Kaplan)Tj /T1_3 1 Tf 3.314 0 Td [(et)-191(al)-30(.)]TJ /T1_1 1 Tf 2.159 0 Td [(\(11\))-191(model,)-191(first)-191(under)-191(trace)-191(vac)-30(cination)-191(and)-191(sec)-30(ond)]TJ -5.472 -1.13 Td [(under)-623(mass)-623(vac)-30(cination,)-623(to)-623(calculate)-623(the)-623(dif)-30(ference)-623(in)-623(the)]TJ T* [(number)-453(of)-453(people)-453(dying)-453(bet)-30(ween)-453(the)-453(t)-30(wo)-453(strategie)20(s)-453(for)-453(each)]TJ T* [(parameter)-375(set.)-375(Our)-375(evaluation)-375(of)-375(the)-375(relative)-375(ef)-30(ficienc)-30(y)-375(of)-375(the)]TJ T* [(t)-30(wo)-329(strategie)20(s)-329(thus)-329(c)-30(onsiders)-329(both)-329(the)-329(most)-329(likely)-329(dif)-30(ference)-329(in)]TJ 0 -1.13 TD [(the)-390(number)-390(dead)-390(and)-390(the)-390(uncert)-30(aint)-30(y)-390(in)-390(the)-390(dif)-30(ference)-390(in)-390(the)]TJ T* [(number)-338(dead.)]TJ /T1_5 1 Tf -0.0196 Tc 0 -2.019 TD [(Results)-313(and)-313(Discussion)]TJ /T1_1 1 Tf 0.005 Tc 0 -1.352 TD [(Our)-301(re)20(sults)-301(show)-301(that)-301(the)-301(overall)-301(uncert)-30(aint)-30(y)-301(in)-301(the)-301(parameters)]TJ 0 -1.13 TD [(of)-390(the)-390(SEIR)-390(model)-390(is)-390(remark)-30(ably)-390(large)-390(\(Table)-390(1\).)-390(Part)-390(of)-390(the)]TJ T* [(reason)-369(is)-369(that,)-369(when)-369(fitting)-369(the)-369(model)-369(to)-369(the)-369(epidemic)-369(dat)-30(a,)-369(it)]TJ 0 -1.13 TD [(bec)-30(ome)20(s)-476(harder)-476(to)-476(distinguish)-476(among)-476(epidemic)-476(cur)-60(ve)20(s)-476(as)]TJ /T1_3 1 Tf 0 Tc 26.469 0 Td (R)Tj /T1_1 1 Tf 6.5 0 0 6 558.4833 155.1676 Tm (0)Tj 0.005 Tc 9 0 0 9 314.1761 146.2471 Tm [(increase)20(s)-532(\(Fig.)-532(1\).)-532(The)-532(prior)-532(uncert)-30(aint)-30(y)-532(in)-532(the)-532(parameters,)]TJ 0 -1.13 TD [(however,)-526(also)-526(c)-30(ontribute)20(s)-526(subst)-30(antially)-526(to)-526(the)-526(overall)-526(uncer-)]TJ T* [(t)-30(aint)-30(y.)-183(To)-183(illustrate)-183(this)-183(ef)-30(fect,)-183(in)-183(Fig.)-183(2)-183(we)-183(show)-183(that)-183(the)-183(marginal)]TJ T* [(distribution)-312(of)]TJ /T1_3 1 Tf 0 Tc 6.527 0 Td (R)Tj /T1_1 1 Tf 6.5 0 0 6 379.0076 114.4858 Tm (0)Tj 0.005 Tc 9 0 0 9 385.1014 115.7358 Tm [(is)-312(much)-312(w)-40(ider)-312(when)-312(we)-312(allow)-312(for)-312(uncert)-30(aint)-30(y)]TJ -7.881 -1.13 Td [(in)-244(all)-244(parameters)-244(than)-244(it)-244(is)-244(when)-244(we)-244(allow)-244(for)-244(uncert)-30(aint)-30(y)-244(only)-244(in)]TJ /T1_3 1 Tf 0 Tc T* (R)Tj /T1_1 1 Tf 6.5 0 0 6 320.2603 94.1448 Tm (0)Tj 0.005 Tc 9 0 0 9 326.5815 95.3949 Tm [(and)-338(the)-338(error)-338(parameter)]TJ /T1_0 1 Tf 0 Tc 9 0 1.3977 9 425.8482 95.3949 Tm (\006)Tj /T1_1 1 Tf 6.5 0 0 6 431.3924 98.3949 Tm (2)Tj 9 0 0 9 434.6738 95.3949 Tm (.)Tj 0.005 Tc -12.389 -1.13 Td [(The)-600(uncert)-30(aint)-30(y)-600(in)-600(the)-600(parameters)-600(has)-600(import)-30(ant)-600(c)-30(onse-)]TJ -1 -1.13 Td [(quence)20(s)-336(for)-336(uncert)-30(aint)-30(y)-336(in)-336(the)-336(relative)-336(ef)-30(fectivene)20(ss)-336(of)-336(the)-336(t)-30(wo)]TJ T* [(vac)-30(cination)-397(strategie)20(s.)-397(When)-397(the)-397(likelihood)-397(is)-397(calculated)-397(f)-30(rom)]TJ /T1_6 1 Tf 0 Tc 8 0 0 8 90.6761 735.3835 Tm [(Table)-333(1.)-333(Prior)-333(and)-333(posterior)-333(medians)-333(\(with)-333(95%)-333(central)-333(credible)-333(intervals,)-333(the)-333(Bayesian)-333(counterpart)-333(to)-333(the)]TJ 0 -1.25 TD [(frequentist\222s)-333(con\036dence)-333(interval\))-333(of)-333(parameters)-333(for)-333(the)-333(SEIR)-333(model)-333(of)-278(smallpox)]TJ ET 0 0 0 1 K 0.5 w 10 M 0 j 0 J []0 d 90.676 580.634 m 522.676 580.634 l 90.676 696.134 m 522.676 696.134 l S BT /T1_7 1 Tf 7.5 0 0 7.5 90.6761 701.3835 Tm [(Parameter)-18742(Prior)]TJ 36.5 1.333 Td (Posterior)Tj -0.834 -1.333 Td [(\(SEIR)-278(model\))]TJ 12.811 1.333 Td [(Posterior)-278(\(SEIR)-278(with)]TJ 1.083 -1.333 Td (heterogeneity\))Tj /T1_8 1 Tf -49.56 -2.067 Td (R)Tj /T1_7 1 Tf 0.0001 Tc 5.5 0 0 5 95.2586 684.8835 Tm (0,)Tj /T1_8 1 Tf 0 Tc 0.834 0 Td (e)Tj /T1_7 1 Tf 7.5 0 0 7.5 256.6705 685.8835 Tm [(4)-278(\(0.7,)-278(23.7\))-7668(7.1)-278(\(5.0,)-278(15.3\))-8224(6.8)-278(\(5.4,)-278(10.4\))]TJ /T1_8 1 Tf -22.133 -1.333 Td (R)Tj /T1_7 1 Tf 0.0001 Tc 5.5 0 0 5 95.2586 674.8835 Tm (0,)Tj /T1_8 1 Tf 0 Tc 0.834 0 Td (u)Tj /T1_7 1 Tf 7.5 0 0 7.5 256.6705 675.8835 Tm [(4)-278(\(0.7,)-278(23.7\))-7112(17.5)-278(\(5.9,)-278(59.5\))-7668(16.3)-278(\(7.2,)-278(36.6\))]TJ /T1_0 1 Tf 7.5 0 1.1648 7.5 90.6761 665.8835 Tm (\006)Tj /T1_8 1 Tf 5.5 0 0 5 95.2586 664.8835 Tm (e)Tj /T1_7 1 Tf 7.5 0 0 7.5 272.0909 665.8835 Tm [(\227)-8893(0.021)-278(\(0.017,)-278(0.032\))-5444(0.021)-278(\(0.017,)-278(0.026\))]TJ /T1_0 1 Tf 7.5 0 1.1648 7.5 90.6761 655.8835 Tm (\006)Tj /T1_8 1 Tf 5.5 0 0 5 95.2586 654.8835 Tm (u)Tj /T1_7 1 Tf 7.5 0 0 7.5 272.0909 655.8835 Tm [(\227)-8893(0.146)-278(\(0.110,)-278(0.222\))-5444(0.139)-278(\(0.110,)-278(0.185\))]TJ -24.189 -1.333 Td [(%)-278(Fatality,)]TJ /T1_0 1 Tf 7.5 0 1.1648 7.5 130.2766 645.8835 Tm (\005)Tj /T1_8 1 Tf 5.5 0 0 5 135.2791 644.8835 Tm (e)Tj /T1_7 1 Tf 7.5 0 0 7.5 246.25 645.8835 Tm [(0.14)-278(\(0.03,)-278(0.35\)*)-6000(0.12)-278(\(0.08,)-278(0.19\))-7112(0.12)-278(\(0.09,)-278(0.16\))]TJ -20.743 -1.333 Td [(%)-278(Fatality,)]TJ /T1_0 1 Tf 7.5 0 1.1648 7.5 130.2766 635.8835 Tm (\005)Tj /T1_8 1 Tf 5.5 0 0 5 135.2791 634.8835 Tm (u)Tj /T1_7 1 Tf 7.5 0 0 7.5 246.25 635.8835 Tm [(0.45)-278(\(0.08,)-278(0.95\)*)-6000(0.37)-278(\(0.30,)-278(0.50\))-7112(0.36)-278(\(0.30,)-278(0.43\))]TJ -20.743 -1.333 Td [(Latency)-278(period\226up)-278(to)-278(prodromal)-5630(12.1)-278(\(7.9,)-278(17.6\))-7112(10.3)-278(\(6.3,)-278(15.9\))-8223(8.8)-278(\(5.8,)-278(13.1\))]TJ 0 -1.333 TD [(Latency)-278(period\226prodromal)-8964(2.5)-278(\(1.3,)-278(4.3\))-8224(2.3)-278(\(1.2,)-278(3.9\))-8780(2.1)-278(\(1.1,)-278(3.7\))]TJ T* [(Infectious)-278(period,)-278(1)]TJ /T1_2 1 Tf 9.002 0 Td (\002)Tj /T1_0 1 Tf 7.5 0 1.1648 7.5 161.9416 605.8835 Tm (\002)Tj /T1_7 1 Tf 7.5 0 0 7.5 246.25 605.8835 Tm [(15.8)-278(\(10.9,)-278(22.0\))-6556(13.4)-278(\(8.8,)-278(19.6\))-7668(11.5)-278(\(7.7,)-278(16.1\))]TJ -20.743 -1.333 Td [(Old)-278(World)-278(heterogeneity)]TJ /T1_8 1 Tf 12.003 0 Td (k)Tj 5.5 0 0 5 184.8693 594.8835 Tm (e)Tj /T1_7 1 Tf 7.5 0 0 7.5 250.4176 595.8835 Tm [(2.8)-278(\(0.10,)-278(14.8\))-10002(\227)-10282(358)-278(\(198,)-278(976\))]TJ -21.299 -1.333 Td [(New)-278(World)-278(heterogeneity)]TJ /T1_8 1 Tf 12.447 0 Td (k)Tj 5.5 0 0 5 188.1993 584.8835 Tm (u)Tj /T1_7 1 Tf 7.5 0 0 7.5 250.4176 585.8835 Tm [(2.8)-278(\(0.10,)-278(14.8\))-10002(\227)-9448(2,712)-278(\(415,)-278(17,579\))]TJ 7 0 0 7 99.6761 570.3835 Tm [(Note)-311(that,)-311(although)-311(the)-311(95%)-311(central)-311(credible)-311(interval)-311(on)]TJ /T1_8 1 Tf 26.974 0 Td (R)Tj /T1_7 1 Tf 5 0 0 5 292.771 569.3835 Tm (0)Tj 7 0 0 7 297.7303 570.3835 Tm [(has)-311(a)-311(smaller)-311(range)-311(for)-311(the)-311(heterogeneity)-311(model)-311(than)-311(for)-311(the)-311(model)]TJ -29.579 -1.286 Td [(without)-200(heterogeneity,)-200(the)-200(median)-200(value)-200(is)-200(approximately)-200(the)-200(same)-200(for)-200(the)-200(two)-200(models.)-200(The)-200(similarity)-200(of)-200(the)-200(medians)-200(suggests)-200(that)-200(the)]TJ 0 -1.286 TD [(major)-293(effect)-293(on)-293(the)-293(marginal)-293(distribution)-293(of)]TJ /T1_8 1 Tf 20.886 0 Td (R)Tj /T1_7 1 Tf 5 0 0 5 241.1526 551.3835 Tm (0)Tj 7 0 0 7 245.9812 552.3835 Tm [(of)-293(allowing)-293(for)-293(heterogeneity)-293(in)-293(susceptibility)-293(is)-293(a)-293(reduction)-293(in)-293(the)-293(long)-293(tail,)-293(which)-293(is)]TJ -22.186 -1.286 Td [(con\036rmed)-403(by)-403(an)-403(examination)-403(of)-403(the)-403(full)-403(distribution)-403(\(see)-403(supporting)-403(information\).)-403(Also,)-403(following)-403(standard)-403(terminology)-403(\(2\),)-403(the)]TJ T* [(heterogeneity)-289(parameter)]TJ /T1_8 1 Tf 12.083 0 Td (k)Tj /T1_7 1 Tf 0.845 0 Td [(is)-289(the)-289(inverse)-289(of)-289(the)-289(squared)-289(coef\036cient)-289(of)-289(variation)-289(of)-289(the)-289(distribution)-289(of)-289(susceptibility.)-289(The)-289(large)-289(values)]TJ -12.928 -1.286 Td [(shown)-333(here)-333(therefore)-333(indicate)-333(very)-333(low)-333(levels)-333(of)-333(heterogeneity.)-333(SEIR)-333(with)-333(heterogeneity)-333(refers)-333(to)-333(a)-333(version)-333(of)-333(the)-333(SEIR)-333(model)-333(that)]TJ T* [(includes)-219(heterogeneity)-219(in)-219(susceptibility)-219(\(see)-219(supporting)-219(information\).)-219(The)-219(prodromal)-219(period)-219(occurs)-219(between)-219(the)-219(onset)-219(of)-219(fever)-219(and)-219(the)]TJ 0 -1.286 TD [(beginning)-300(of)-300(a)-300(rash.)-300(The)-300(subscript)]TJ /T1_8 1 Tf 16.193 0 Td (e)Tj /T1_7 1 Tf 0.856 0 Td [(stands)-300(for)-300(exposed,)-300(Old)-300(World)-300(populations,)-300(whereas)-300(the)-300(subscript)]TJ /T1_8 1 Tf 31.096 0 Td (u)Tj /T1_7 1 Tf 0.911 0 Td [(stands)-300(for)-300(unexposed,)-300(New)]TJ -49.057 -1.286 Td [(World)-278(populations.)]TJ T* [(*Intervals)-278(based)-278(on)-278(500,000)-278(simulated)-278(draws)-278(from)-278(a)-278(mixture)-278(re\037ecting)-278(the)-278(hyperprior)-278(structure.)]TJ /T1_6 1 Tf 6.5 0 0 6.5 51.6761 39.8835 Tm (15694)Tj /T1_2 1 Tf 9.75 0 0 6.5 75.7468 39.8835 Tm (\001)Tj /T1_7 1 Tf 6.5 0 0 6.5 83.9114 39.8835 Tm (www.pnas.org)Tj /T1_2 1 Tf 6.833 0 Td (\002)Tj /T1_7 1 Tf 0.5 0 Td 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[(sponding)-480(predictions)-480(of)-480(more)-480(c)-30(omplex)-480(models)-480(may)-480(be)-480(more)]TJ T* [(ac)-30(curate)-563(\(16\).)-563(Neverthele)20(ss,)-563(any)-563(such)-563(advant)-30(age)-563(of)-563(a)-563(more)]TJ T* [(c)-30(omplex)-193(model)-193(may)-193(be)-193(out)-30(weighed)-193(by)-193(an)-193(increase)-193(in)-193(uncert)-30(aint)-30(y,)]TJ T* [(because)-261(the)-261(good)-261(fit)-261(of)-261(the)-261(SEIR)-261(model)-261(to)-261(smallpox)-261(dat)-30(a)-261(means)]TJ T* [(that)-292(a)-292(more)-292(c)-30(omplex)-292(model)-292(would)-292(not)-292(fit)-292(the)-292(dat)-30(a)-292(much)-292(better.)]TJ T* [(To)-214(illustrate)-214(this)-214(point,)-214(we)-214(extended)-214(the)-214(SEIR)-214(model)-214(to)-214(allow)-214(for)]TJ T* [(heterogeneit)-30(y)-576(in)-576(susceptibilit)-30(y)-576(\(see)-576(supporting)-576(infor)-30(mation\),)]TJ T* [(which)-224(is)-224(w)-40(idely)-224(believed)-224(to)-224(be)-224(import)-30(ant)-224(in)-224(disease)-224(dynamics)-224(\(2\),)]TJ T* [(and)-333(repeated)-333(our)-333(Baye)20(sian)-333(calculation.)-333(The)-333(levels)-333(of)-333(heteroge-)]TJ T* [(neit)-30(y)-295(in)-295(susceptibilit)-30(y)-295(needed)-295(to)-295(ex)-30(plain)-295(the)-295(dat)-30(a)-295(are)-295(ver)-60(y)-295(small)]TJ T* [(\(Table)-489(1\),)-489(sugge)20(sting)-489(that)-489(the)-489(additional)-489(parameter)-489(prov)-40(ide)20(s)]TJ T* [(little)-585(additional)-585(ex)-30(planator)-60(y)-585(power)-585(and,)-585(therefore,)-585(that)-585(the)]TJ 0 -1.116 TD [(model)-410(w)-40(ithout)-410(heterogeneit)-30(y)-410(is)-410(suf)-30(ficient)-410(to)-410(ex)-30(plain)-410(the)-410(dat)-30(a.)]TJ 0 -1.116 TD [(Moreover,)-618(for)-618(the)-618(model)-618(w)-40(ith)-618(heterogeneit)-30(y,)-618(the)-618(marginal)]TJ T* [(distribution)-349(of)]TJ /T1_2 1 Tf 0 Tc 6.601 0 Td (R)Tj /T1_0 1 Tf 6.5 0 0 6 117.1667 103.8153 Tm (0)Tj 0.005 Tc 9 0 0 9 123.5901 105.0653 Tm [(is)-349(ver)-60(y)-349(similar)-349(to)-349(that)-349(for)-349(the)-349(model)-349(w)-40(ithout)]TJ -7.99 -1.116 Td [(heterogeneit)-30(y;)-430(as)-430(Table)-430(1)-430(shows,)-430(the)-430(main)-430(ef)-30(fect)-430(is)-430(a)-430(mode)20(st)]TJ 0 -1.116 TD [(reduction)-400(in)-400(the)-400(t)-30(ail)-400(of)-400(the)-400(distribution)-400(\(see)-400(supporting)-400(infor-)]TJ T* [(mation)-264(for)-264(the)-264(full)-264(distribution.)-264(Note)-264(that,)-264(for)-264(the)-264(heterogeneit)-30(y)]TJ T* [(model,)-312(the)-312(parameter)]TJ /T1_2 1 Tf 0 Tc 9.757 0 Td (R)Tj /T1_0 1 Tf 6.5 0 0 6 145.5748 63.6335 Tm (0)Tj 0.005 Tc 9 0 0 9 151.663 64.8835 Tm [(is)-312(actually)]TJ /T1_2 1 Tf 0 Tc 4.62 0 Td (R)Tj /T1_3 1 Tf 0.169 0.2 Td (\001)Tj /T1_0 1 Tf 6.5 0 0 6 199.3305 63.6335 Tm (0)Tj 0.005 Tc 9 0 0 9 202.6118 64.8835 Tm [(,)-312(the)-312(average)-312(value)-312(of)]TJ /T1_2 1 Tf 0 Tc 9.7 0 Td (R)Tj /T1_0 1 Tf 6.5 0 0 6 295.9954 63.6335 Tm (0)Tj 0.005 Tc 9 0 0 9 314.1761 301.8835 Tm [(across)-591(host)-591(indiv)-40(iduals.)-591(For)-591(c)-30(onven)-30(ience,)-591(we)-591(refer)-591(to)-591(both)]TJ 0 -1.145 TD [(parameters)-443(simply)-443(as)]TJ /T1_2 1 Tf 0 Tc 9.853 0 Td (R)Tj /T1_0 1 Tf 6.5 0 0 6 408.9384 290.3267 Tm (0)Tj 0.005 Tc 9 0 0 9 412.2197 291.5767 Tm [(\).)-443(As)-443(a)-443(re)20(sult,)-443(the)-443(uncert)-30(aint)-30(y)-443(in)-443(the)]TJ -10.894 -1.145 Td [(ef)-30(fectivene)20(ss)-287(of)-287(the)-287(t)-30(wo)-287(vac)-30(cination)-287(strategie)20(s)-287(ver)-60(y)-287(nearly)-287(is)-287(the)]TJ T* [(same)-546(for)-546(the)-546(t)-30(wo)-546(models)-546(\(supporting)-546(infor)-30(mation\).)-546(Indeed,)]TJ T* [(under)-234(the)-234(heterogeneit)-30(y)-234(model,)-234(the)-234(chance)-234(that)-234(the)-234(exce)20(ss)-234(in)-234(the)]TJ T* [(number)-339(of)-339(deaths)-339(under)-339(trace)-339(vac)-30(cination)-339(is)-339(at)-339(least)-339(200,000)-339(is)]TJ T* [(15%,)-325(which)-325(is)-325(close)-325(to)-325(the)-325(value)-325(of)-325(17%)-325(for)-325(the)-325(model)-325(w)-40(ithout)]TJ T* [(heterogeneit)-30(y)-320(\(see)-320(supporting)-320(infor)-30(mation)-320(for)-320(the)-320(full)-320(distribu-)]TJ 0 -1.145 TD [(tion)-436(of)-436(outc)-30(ome)20(s)-436(under)-436(the)-436(heterogeneit)-30(y)-436(model\).)-436(Increasing)]TJ 0 -1.145 TD [(realism)-549(still)-549(further,)-549(to)-549(enc)-30(ompass)-549(the)-549(tens)-549(to)-549(hundreds)-549(of)]TJ T* [(parameters)-396(of)-396(c)-30(omplex)-396(models)-396(\(4)-90(\226)-90(6\),)-396(might)-396(well)-396(increase)-396(the)]TJ T* [(uncert)-30(aint)-30(y,)-290(because)-290(any)-290(small)-290(decrease)-290(in)-290(uncert)-30(aint)-30(y)-290(due)-290(to)-290(a)]TJ T* [(slight)-302(improvement)-302(in)-302(the)-302(fit)-302(to)-302(dat)-30(a)-302(would)-302(be)-302(out)-30(weighed)-302(by)-302(a)]TJ T* [(large)-532(increase)-532(in)-532(uncert)-30(aint)-30(y)-532(due)-532(to)-532(fitting)-532(many)-532(additional)]TJ T* [(parameters.)-501(When)-501(uncert)-30(aint)-30(y)-501(e)20(stimate)20(s)-501(are)-501(made)-501(for)-501(other)]TJ T* [(disease)20(s,)-265(however,)-265(enough)-264(dat)-30(a)-265(may)-265(be)-265(available)-265(to)-265(justif)-30(y)-265(more)]TJ T* [(c)-30(omplex)-338(models)-338(\(7,)-338(8,)-338(10,)-338(17,)-338(18\).)]TJ 1 -1.145 Td [(A)-388(related)-388(point)-388(is)-388(that)-388(we)-388(have)-388(c)-30(onsidered)-388(only)-388(t)-30(wo)-388(simple)]TJ -1 -1.145 Td [(vac)-30(cination)-429(scheme)20(s,)-429(yet)-429(some)-429(authors)-429(have)-429(argued)-429(for)-429(more)]TJ 0 -1.144 TD [(c)-30(omplex)-279(re)20(sponse)20(s)-279(\(4\),)-279(such)-279(as)-279(vac)-30(cinations)-279(that)-279(are)-279(t)-30(argeted)-279(at)]TJ T* [(particular)-213(spatial)-213(locations.)-213(Such)-213(arguments,)-213(however,)-213(have)-213(been)]TJ T* [(based)-355(on)-355(c)-30(omplex)-355(models,)-355(for)-355(which)-355(rigorous)-355(uncert)-30(aint)-30(y)-355(e)20(sti-)]TJ T* [(mate)20(s)-283(are)-283(unavailable.)-283(As)-283(we)-283(have)-283(shown,)-283(for)-30(mally)-283(allow)-40(ing)-283(for)]TJ T* [(uncert)-30(aint)-30(y)-222(can)-222(reveal)-222(hidden)-222(risks)-222(of)-222(vac)-30(cination)-222(strategie)20(s,)-222(and)]TJ ET /Document /MC0 BDC 0 0 0 0 k 80.059 737.984 212.534 -167.694 re f 0 0 0 0 K 0.238 w 10 M 1 j 0 J []0 d /GS1 gs 80.059 570.291 m 80.059 737.984 l 292.593 737.984 l 292.593 570.291 l 80.059 570.291 l S 0 0 0 1 K 80.059 570.291 m 80.059 572.433 l 80.059 570.291 m 80.059 737.984 l 80.059 570.291 m 292.593 570.291 l S 0 g BT /T1_4 1 Tf 0 Tc 5.2747 0 0 5.2747 78.7498 564.5366 Tm (0)Tj ET 115.455 570.291 m 115.455 572.433 l S BT /T1_4 1 Tf 0.0001 Tc 5.2747 0 0 5.2747 111.4876 564.5366 Tm (100)Tj ET 150.89 570.291 m 150.89 572.433 l S BT /T1_4 1 Tf 5.2747 0 0 5.2747 146.9232 564.5366 Tm (200)Tj ET 186.326 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232.753 640.408 l 233.824 641.32 l 234.896 642.154 l 235.968 643.027 l 238.11 644.615 l 239.181 645.368 l 240.253 646.081 l 241.325 646.796 l 242.395 647.471 l 243.428 648.106 l 244.5 648.741 l 245.571 649.376 l 246.642 649.931 l 247.714 650.487 l 248.785 651.042 l 249.856 651.558 l 250.927 652.035 l 251.999 652.511 l 253.071 652.947 l 254.142 653.383 l 255.174 653.82 l 256.245 654.217 l 257.317 654.574 l 258.387 654.931 l 259.459 655.289 l 260.531 655.606 l 261.602 655.923 l 262.673 656.241 l 263.744 656.518 l 264.816 656.796 l 265.887 657.035 l 266.96 657.272 l 267.99 657.51 l 269.061 657.748 l 270.133 657.947 l 271.205 658.145 l 272.276 658.344 l 273.347 658.542 l 274.42 658.701 l 275.49 658.859 l 276.561 659.018 l 277.633 659.177 l 278.705 659.335 l 279.775 659.455 l 280.807 659.574 l 281.879 659.733 l 282.951 659.852 l 284.022 659.931 l 285.094 660.05 l 286.165 660.129 l 287.237 660.249 l 288.308 660.328 l 289.38 660.407 l 290.451 660.487 l 292.593 660.645 l S Q BT /T1_4 1 Tf 0 Tc 0.0001 Tw 8.5712 0 0 8.5712 163.7481 550.7095 Tm (Time \(days\))Tj 0.0001 Tc -0.0001 Tw 0 8.5712 -8.5712 0 59.7889 627.5126 Tm (Number Dead)Tj /T1_5 1 Tf 0 Tc 0 Tw 7.6188 0 0 7.6188 87.1234 711.079 Tm (R)Tj /T1_4 1 Tf 5.7141 0 0 5.7141 92.5994 707.27 Tm (o)Tj -0.0002 Tw 7.6188 0 0 7.6188 95.7738 711.079 Tm ( = 9 )Tj /T1_6 1 Tf 0 Tw 1.974 0 Td (\001)Tj 16.885 -9.172 Td (\002)Tj /T1_4 1 Tf 0.984 0 Td ( )Tj /T1_5 1 Tf 8.3819 0 0 8.3819 249.0771 641.2006 Tm (R)Tj /T1_4 1 Tf 5.7141 0 0 5.7141 254.5791 637.3915 Tm (o)Tj -0.0001 Tw 7.6188 0 0 7.6188 257.7531 641.2006 Tm ( = 2)Tj ET EMC 0 0 0 1 k /GS0 gs BT /T1_7 1 Tf 0 Tw 7 0 0 7 51.6761 532.8835 Tm [(Fig.)-271(1.)]TJ /T1_8 1 Tf 4.042 0 Td [(Impact)-271(of)-271(changing)]TJ /T1_9 1 Tf 9.312 0 Td (R)Tj /T1_8 1 Tf 5 0 0 5 149.436 531.8835 Tm (0)Tj 7 0 0 7 154.1113 532.8835 Tm [(on)-271(epidemic)-271(dynamics)-271(in)-271(the)-271(SEIR)-271(model)-271(\(Eq.)]TJ /T1_7 1 Tf -14.634 -1.286 Td (1)Tj /T1_8 1 Tf 0.556 0 Td [(\).)-183(All)-183(other)-183(parameters)-183(are)-183(\036xed.)-183(As)]TJ /T1_9 1 Tf 16.228 0 Td (R)Tj /T1_8 1 Tf 5 0 0 5 173.439 522.8835 Tm (0)Tj 7 0 0 7 177.4977 523.8835 Tm [(increases)-183(\(by)-183(ones)-183(from)-183(one)-183(line)-183(to)-183(the)]TJ -17.974 -1.286 Td [(next\),)-278(the)-278(cumulative)-278(death)-278(curves)-278(are)-278(increasingly)-278(similar.)]TJ ET /Document /MC1 BDC 0.332 w 1 J /GS1 gs 546.578 639.678 m 546.578 635.699 l 447.258 639.678 m 447.258 635.699 l 347.936 639.678 m 347.936 635.699 l 347.936 639.678 m 554.854 639.678 l S 0 g BT /T1_4 1 Tf 6.6319 0 0 6.632 543.4841 625.7955 Tm (20)Tj -15 0 Td (10)Tj -14.81 0 Td (0)Tj ET 347.936 718.391 m 343.957 718.391 l 347.936 679.037 m 343.957 679.037 l 347.936 639.678 m 343.957 639.678 l 347.936 639.678 m 347.936 718.391 l S BT /T1_4 1 Tf 0 6.632 -6.6319 0 338.3065 637.8345 Tm [(0)-4684(0.25)-4266(0.5)]TJ ET q 316.926 469.884 241.866 270.079 re W n 347.936 639.678 m 347.936 738.676 l S 0 0 0 0.202 K 383.953 639.678 m 383.953 639.678 l 383.771 639.678 m 383.771 639.678 l 383.59 639.678 m 383.59 639.678 l 383.413 639.678 m 383.413 639.678 l 383.232 639.678 m 383.232 639.678 l 383.05 639.678 m 383.05 639.678 l 382.869 639.678 m 382.869 639.678 l 382.692 639.678 m 382.692 639.678 l 382.511 639.678 m 382.511 639.678 l 382.33 639.678 m 382.33 639.678 l 382.152 639.678 m 382.152 639.678 l 381.972 639.678 m 381.972 639.678 l 381.79 639.678 m 381.79 639.678 l 381.609 639.678 m 381.609 639.678 l 381.432 639.678 m 381.432 639.678 l 381.251 639.678 m 381.251 639.678 l 381.07 639.678 m 381.07 639.678 l 380.888 639.678 m 380.888 639.678 l 380.711 639.678 m 380.711 639.678 l 380.531 639.678 m 380.531 639.678 l 380.349 639.678 m 380.349 639.678 l 380.172 639.678 m 380.172 639.678 l 379.991 639.678 m 379.991 639.678 l 379.809 639.678 m 379.809 639.678 l 379.628 639.678 m 379.628 639.678 l 379.451 639.678 m 379.451 639.678 l 379.27 639.678 m 379.27 639.678 l 379.089 639.678 m 379.089 639.678 l 378.908 639.678 m 378.908 639.678 l 378.731 639.678 m 378.731 639.678 l 378.55 639.678 m 378.55 639.678 l 378.368 639.678 m 378.368 639.678 l 378.192 639.678 m 378.192 639.678 l 378.01 639.678 m 378.01 639.678 l 377.829 639.678 m 377.829 639.678 l 377.647 639.678 m 377.647 639.678 l 377.47 639.678 m 377.47 639.678 l 377.289 639.678 m 377.289 639.678 l 377.108 639.678 m 377.108 639.678 l 376.926 639.678 m 376.926 639.678 l 376.749 639.678 m 376.749 639.678 l 376.569 639.678 m 376.569 639.678 l 376.388 639.678 m 376.388 639.678 l 376.211 639.678 m 376.211 639.678 l 376.029 639.678 m 376.029 639.678 l 375.848 639.678 m 375.848 639.678 l 375.667 639.678 m 375.667 639.678 l 375.49 639.678 m 375.49 639.678 l 375.309 639.678 m 375.309 639.678 l 375.127 639.678 m 375.127 639.678 l 374.946 639.678 m 374.946 639.678 l 374.769 639.678 m 374.769 639.678 l 374.587 639.678 m 374.587 639.678 l 374.407 639.678 m 374.407 639.678 l 374.226 639.678 m 374.226 639.678 l 374.049 639.678 m 374.049 639.678 l 373.867 639.678 m 373.867 639.678 l 373.686 639.678 m 373.686 639.678 l 373.509 639.678 m 373.509 639.678 l 373.328 639.678 m 373.328 639.678 l 373.146 639.678 m 373.146 639.678 l 372.965 639.678 m 372.965 639.678 l 372.788 639.678 m 372.788 639.678 l 372.607 639.678 m 372.607 639.678 l 372.426 639.678 m 372.426 639.678 l 372.244 639.678 m 372.244 639.678 l 372.067 639.678 m 372.067 639.678 l 371.887 639.678 m 371.887 639.678 l 371.706 639.678 m 371.706 639.678 l 371.528 639.678 m 371.528 639.678 l 371.347 639.678 m 371.347 639.678 l 371.166 639.678 m 371.166 639.678 l 370.985 639.678 m 370.985 639.678 l 370.808 639.678 m 370.808 639.678 l 370.626 639.678 m 370.626 639.678 l 370.445 639.678 m 370.445 639.678 l 370.264 639.678 m 370.264 639.678 l 370.087 639.678 m 370.087 639.678 l 369.905 639.678 m 369.905 639.678 l 369.724 639.678 m 369.724 639.678 l 369.547 639.678 m 369.547 639.678 l 369.367 639.678 m 369.367 639.678 l 369.185 639.678 m 369.185 639.678 l 369.004 639.678 m 369.004 639.678 l 368.827 639.678 m 368.827 639.678 l 368.646 639.678 m 368.646 639.678 l 368.464 639.678 m 368.464 639.678 l 368.283 639.678 m 368.283 639.678 l 368.106 639.678 m 368.106 639.678 l 367.925 639.678 m 367.925 639.678 l 367.744 639.678 m 367.744 639.678 l 367.562 639.678 m 367.562 639.678 l 367.385 639.678 m 367.385 639.678 l 367.205 639.678 m 367.205 639.678 l 367.023 639.678 m 367.023 639.678 l 366.846 639.678 m 366.846 639.678 l 366.665 639.678 m 366.665 639.678 l 366.484 639.678 m 366.484 639.678 l 366.303 639.678 m 366.303 639.678 l 366.125 639.678 m 366.125 639.678 l 365.944 639.678 m 365.944 639.678 l 365.763 639.678 m 365.763 639.678 l 365.582 639.678 m 365.582 639.678 l 365.405 639.678 m 365.405 639.678 l 365.223 639.678 m 365.223 639.678 l 365.042 639.678 m 365.042 639.678 l 364.865 639.678 m 364.865 639.678 l 364.685 639.678 m 364.685 639.678 l 364.503 639.678 m 364.503 639.678 l 364.322 639.678 m 364.322 639.678 l 364.145 639.678 m 364.145 639.678 l 363.964 639.678 m 363.964 639.678 l 363.782 639.678 m 363.782 639.678 l 363.601 639.678 m 363.601 639.678 l 363.424 639.678 m 363.424 639.678 l 363.243 639.678 m 363.243 639.678 l 363.061 639.678 m 363.061 639.678 l 362.885 639.678 m 362.885 639.678 l 362.703 639.678 m 362.703 639.678 l 362.522 639.678 m 362.522 639.678 l 362.341 639.678 m 362.341 639.678 l 362.164 639.678 m 362.164 639.678 l 361.983 639.678 m 361.983 639.678 l 361.802 639.678 m 361.802 639.678 l 361.621 639.678 m 361.621 639.678 l 361.443 639.678 m 361.443 639.678 l 361.262 639.678 m 361.262 639.678 l 361.08 639.678 m 361.08 639.678 l 360.904 639.678 m 360.904 639.678 l 360.723 639.678 m 360.723 639.678 l 360.541 639.678 m 360.541 639.678 l 360.36 639.678 m 360.36 639.678 l 360.184 639.678 m 360.184 639.678 l 360.002 639.678 m 360.002 639.678 l 359.821 639.678 m 359.821 639.678 l 359.64 639.678 m 359.64 639.678 l 359.462 639.678 m 359.462 639.678 l 359.282 639.678 m 359.282 639.678 l 359.1 639.678 m 359.1 639.678 l 358.918 639.678 m 358.918 639.678 l 358.742 639.678 m 358.742 639.678 l 358.56 639.678 m 358.56 639.678 l 358.379 639.678 m 358.379 639.678 l 358.203 639.678 m 358.203 639.678 l 358.021 639.678 m 358.021 639.678 l 357.84 639.678 m 357.84 639.678 l 357.659 639.678 m 357.659 639.678 l 357.482 639.678 m 357.482 639.678 l 357.301 639.678 m 357.301 639.678 l 357.12 639.678 m 357.12 639.678 l 356.938 639.678 m 356.938 639.678 l 356.761 639.678 m 356.761 639.678 l 356.58 639.678 m 356.58 639.678 l 356.398 639.678 m 356.398 639.678 l 356.222 639.678 m 356.222 639.678 l 356.04 639.678 m 356.04 639.678 l 355.859 639.678 m 355.859 639.678 l 355.677 639.678 m 355.677 639.678 l 355.501 639.678 m 355.501 639.678 l 355.32 639.678 m 355.32 639.678 l 355.139 639.678 m 355.139 639.678 l 354.957 639.678 m 354.957 639.678 l 354.781 639.678 m 354.781 639.678 l 354.599 639.678 m 354.599 639.678 l 354.418 639.678 m 354.418 639.678 l 354.241 639.678 m 354.241 639.678 l 354.06 639.678 m 354.06 639.678 l 353.878 639.678 m 353.878 639.678 l 353.697 639.678 m 353.697 639.678 l 353.52 639.678 m 353.52 639.678 l 353.339 639.678 m 353.339 639.678 l 353.158 639.678 m 353.158 639.678 l 352.976 639.678 m 352.976 639.678 l 352.799 639.678 m 352.799 639.678 l 352.618 639.678 m 352.618 639.678 l 352.437 639.678 m 352.437 639.678 l 352.26 639.678 m 352.26 639.678 l 352.079 639.678 m 352.079 639.678 l 351.897 639.678 m 351.897 639.678 l 351.716 639.678 m 351.716 639.678 l 351.539 639.678 m 351.539 639.678 l 351.358 639.678 m 351.358 639.678 l 351.177 639.678 m 351.177 639.678 l 350.996 639.678 m 350.996 639.678 l 350.819 639.678 m 350.819 639.678 l 350.637 639.678 m 350.637 639.678 l 350.456 639.678 m 350.456 639.678 l 350.275 639.678 m 350.275 639.678 l 350.098 639.678 m 350.098 639.678 l 349.917 639.678 m 349.917 639.678 l 349.736 639.678 m 349.736 639.678 l 349.559 639.678 m 349.559 639.678 l 349.377 639.678 m 349.377 639.678 l 349.196 639.678 m 349.196 639.678 l 349.015 639.678 m 349.015 639.678 l 348.838 639.678 m 348.838 639.678 l 348.657 639.678 m 348.657 639.678 l 348.476 639.678 m 348.476 639.678 l 348.294 639.678 m 348.294 639.678 l 348.117 639.678 m 348.117 639.678 l S 410.012 691.129 m 413.677 694.795 l 410.012 691.311 m 413.496 694.795 l 410.012 691.487 m 413.319 694.795 l 410.012 691.669 m 413.138 694.795 l 410.012 691.85 m 412.956 694.795 l 410.012 692.031 m 412.775 694.795 l 410.012 692.208 m 412.598 694.795 l 410.012 692.389 m 412.417 694.795 l 410.012 692.57 m 412.236 694.795 l 410.012 692.752 m 412.059 694.795 l 410.012 692.929 m 411.877 694.795 l 410.012 693.11 m 411.696 694.795 l 410.012 693.292 m 411.515 694.795 l 410.012 693.468 m 411.338 694.795 l 410.012 693.65 m 411.157 694.795 l 410.012 693.83 m 410.976 694.795 l 410.012 694.012 m 410.794 694.795 l 410.012 694.189 m 410.618 694.795 l 410.012 694.37 m 410.436 694.795 l 410.012 694.551 m 410.255 694.795 l 410.012 694.733 m 410.074 694.795 l 409.884 639.678 m 410.012 639.807 l 409.702 639.678 m 410.012 639.987 l 409.521 639.678 m 410.012 640.169 l 409.344 639.678 m 410.012 640.346 l 409.163 639.678 m 410.012 640.527 l 408.981 639.678 m 410.012 640.708 l 408.804 639.678 m 410.012 640.885 l 408.623 639.678 m 410.012 641.066 l 408.442 639.678 m 410.012 641.248 l 408.261 639.678 m 410.012 641.428 l 408.083 639.678 m 410.012 641.606 l 407.902 639.678 m 410.012 641.787 l 407.722 639.678 m 410.012 641.968 l 407.54 639.678 m 410.012 642.15 l 407.363 639.678 m 410.012 642.326 l 407.182 639.678 m 410.012 642.508 l 407.001 639.678 m 410.012 642.689 l 406.82 639.678 m 410.012 642.871 l 406.643 639.678 m 410.012 643.047 l 406.461 639.678 m 410.012 643.229 l 406.28 639.678 m 410.012 643.41 l 406.103 639.678 m 410.012 643.587 l 405.922 639.678 m 410.012 643.767 l 405.74 639.678 m 410.012 643.949 l 405.56 639.678 m 410.012 644.13 l 405.383 639.678 m 410.012 644.307 l 405.202 639.678 m 410.012 644.489 l 405.02 639.678 m 410.012 644.67 l 404.839 639.678 m 410.012 644.851 l 404.662 639.678 m 410.012 645.028 l 404.481 639.678 m 410.012 645.21 l 404.299 639.678 m 410.012 645.391 l 404.122 639.678 m 410.012 645.567 l 403.941 639.678 m 409.856 645.594 l 403.76 639.678 m 409.676 645.594 l 403.579 639.678 m 409.494 645.594 l 403.401 639.678 m 409.317 645.594 l 403.22 639.678 m 409.136 645.594 l 403.114 639.754 m 408.955 645.594 l 403.114 639.935 m 408.774 645.594 l 403.114 640.111 m 408.597 645.594 l 403.114 640.293 m 408.415 645.594 l 403.114 640.474 m 408.234 645.594 l 403.114 640.651 m 408.053 645.594 l 403.114 640.832 m 407.876 645.594 l 403.114 641.013 m 407.695 645.594 l 403.114 641.195 m 407.513 645.594 l 403.114 641.371 m 407.337 645.594 l 403.114 641.553 m 407.155 645.594 l 403.114 641.734 m 406.974 645.594 l 403.114 641.916 m 406.792 645.594 l 403.114 642.092 m 406.616 645.594 l 403.114 642.274 m 406.435 645.594 l 403.114 642.455 m 406.253 645.594 l 403.114 642.632 m 406.072 645.594 l 403.114 642.813 m 405.895 645.594 l 403.114 642.994 m 405.714 645.594 l 403.114 643.175 m 405.533 645.594 l 403.114 643.352 m 405.356 645.594 l 403.114 643.533 m 405.174 645.594 l 403.114 643.714 m 404.994 645.594 l 403.114 643.896 m 404.812 645.594 l 403.114 644.073 m 404.635 645.594 l 403.114 644.254 m 404.454 645.594 l 403.114 644.436 m 404.272 645.594 l 403.114 644.617 m 404.092 645.594 l 403.114 644.794 m 403.914 645.594 l 403.114 644.975 m 403.733 645.594 l 403.114 645.156 m 403.552 645.594 l 403.114 645.333 m 403.375 645.594 l 403.114 645.514 m 403.194 645.594 l 403.039 639.678 m 403.114 639.754 l 402.858 639.678 m 403.105 639.921 l 402.681 639.678 m 402.924 639.921 l 402.5 639.678 m 402.743 639.921 l 402.319 639.678 m 402.566 639.921 l 402.142 639.678 m 402.385 639.921 l 401.96 639.678 m 402.204 639.921 l 401.779 639.678 m 402.022 639.921 l 401.598 639.678 m 401.846 639.921 l 401.421 639.678 m 401.664 639.921 l 401.24 639.678 m 401.483 639.921 l 401.058 639.678 m 401.306 639.921 l 400.877 639.678 m 401.124 639.921 l 400.7 639.678 m 400.943 639.921 l 400.519 639.678 m 400.762 639.921 l 400.338 639.678 m 400.585 639.921 l 400.161 639.678 m 400.404 639.921 l 399.98 639.678 m 400.223 639.921 l 399.798 639.678 m 400.042 639.921 l 399.617 639.678 m 399.865 639.921 l 399.44 639.678 m 399.684 639.921 l 399.259 639.678 m 399.502 639.921 l 399.078 639.678 m 399.321 639.921 l 398.896 639.678 m 399.144 639.921 l 398.719 639.678 m 398.963 639.921 l 398.538 639.678 m 398.781 639.921 l 398.357 639.678 m 398.604 639.921 l 398.176 639.678 m 398.423 639.921 l 397.999 639.678 m 398.242 639.921 l 397.817 639.678 m 398.061 639.921 l 397.637 639.678 m 397.884 639.921 l 397.459 639.678 m 397.703 639.921 l 397.278 639.678 m 397.521 639.921 l 397.097 639.678 m 397.34 639.921 l 396.915 639.678 m 397.163 639.921 l 396.739 639.678 m 396.982 639.921 l 396.558 639.678 m 396.801 639.921 l 396.376 639.678 m 396.624 639.921 l 396.217 639.7 m 396.442 639.921 l 396.217 639.877 m 396.261 639.921 l 396.195 639.678 m 396.195 639.678 l 396.018 639.678 m 396.018 639.678 l 395.837 639.678 m 395.837 639.678 l 395.656 639.678 m 395.656 639.678 l 395.478 639.678 m 395.478 639.678 l 395.298 639.678 m 395.298 639.678 l 395.116 639.678 m 395.116 639.678 l 394.935 639.678 m 394.935 639.678 l 394.758 639.678 m 394.758 639.678 l 394.577 639.678 m 394.577 639.678 l 394.395 639.678 m 394.395 639.678 l 394.214 639.678 m 394.214 639.678 l 394.037 639.678 m 394.037 639.678 l 393.855 639.678 m 393.855 639.678 l 393.675 639.678 m 393.675 639.678 l 393.497 639.678 m 393.497 639.678 l 393.317 639.678 m 393.317 639.678 l 393.135 639.678 m 393.135 639.678 l 392.955 639.678 m 392.955 639.678 l 392.777 639.678 m 392.777 639.678 l 392.596 639.678 m 392.596 639.678 l 392.414 639.678 m 392.414 639.678 l 392.233 639.678 m 392.233 639.678 l 392.057 639.678 m 392.057 639.678 l 391.875 639.678 m 391.875 639.678 l 391.694 639.678 m 391.694 639.678 l 391.517 639.678 m 391.517 639.678 l 391.336 639.678 m 391.336 639.678 l 391.155 639.678 m 391.155 639.678 l 390.974 639.678 m 390.974 639.678 l 390.796 639.678 m 390.796 639.678 l 390.616 639.678 m 390.616 639.678 l 390.434 639.678 m 390.434 639.678 l 390.253 639.678 m 390.253 639.678 l 390.076 639.678 m 390.076 639.678 l 389.894 639.678 m 389.894 639.678 l 389.713 639.678 m 389.713 639.678 l 389.532 639.678 m 389.532 639.678 l 389.355 639.678 m 389.355 639.678 l 389.173 639.678 m 389.173 639.678 l 388.993 639.678 m 388.993 639.678 l 388.815 639.678 m 388.815 639.678 l 388.635 639.678 m 388.635 639.678 l 388.453 639.678 m 388.453 639.678 l 388.272 639.678 m 388.272 639.678 l 388.095 639.678 m 388.095 639.678 l 387.914 639.678 m 387.914 639.678 l 387.732 639.678 m 387.732 639.678 l 387.552 639.678 m 387.552 639.678 l 387.374 639.678 m 387.374 639.678 l 387.193 639.678 m 387.193 639.678 l 387.012 639.678 m 387.012 639.678 l 386.834 639.678 m 386.834 639.678 l 386.654 639.678 m 386.654 639.678 l 386.472 639.678 m 386.472 639.678 l 386.291 639.678 m 386.291 639.678 l 386.114 639.678 m 386.114 639.678 l 385.934 639.678 m 385.934 639.678 l 385.752 639.678 m 385.752 639.678 l 385.571 639.678 m 385.571 639.678 l 385.393 639.678 m 385.393 639.678 l 385.213 639.678 m 385.213 639.678 l 385.031 639.678 m 385.031 639.678 l 384.854 639.678 m 384.854 639.678 l 384.673 639.678 m 384.673 639.678 l 384.491 639.678 m 384.491 639.678 l 384.31 639.678 m 384.31 639.678 l 384.133 639.678 m 384.133 639.678 l S 410.012 655.113 m 416.909 662.01 l 410.012 655.294 m 416.909 662.192 l 410.012 655.475 m 416.909 662.373 l 410.012 655.652 m 416.909 662.55 l 410.012 655.834 m 416.909 662.731 l 410.012 656.015 m 416.909 662.912 l 410.012 656.192 m 416.909 663.089 l 410.012 656.373 m 416.909 663.271 l 410.012 656.554 m 416.909 663.451 l 410.012 656.736 m 416.909 663.633 l 410.012 656.913 m 416.909 663.81 l 410.012 657.094 m 416.909 663.991 l 410.012 657.275 m 416.909 664.172 l 410.012 657.457 m 416.909 664.354 l 410.012 657.633 m 416.909 664.53 l 410.012 657.814 m 416.909 664.712 l 410.012 657.995 m 416.909 664.893 l 410.012 658.172 m 416.909 665.07 l 410.012 658.354 m 416.909 665.251 l 410.012 658.535 m 416.909 665.432 l 410.012 658.716 m 416.909 665.614 l 410.012 658.893 m 416.909 665.79 l 410.012 659.075 m 416.909 665.972 l 410.012 659.256 m 416.909 666.153 l 410.012 659.437 m 416.909 666.335 l 410.012 659.614 m 416.909 666.511 l 410.012 659.796 m 416.909 666.692 l 410.012 659.977 m 416.909 666.874 l 410.012 660.157 m 416.909 667.055 l 410.012 660.334 m 416.909 667.233 l 410.012 660.516 m 416.909 667.413 l 410.012 660.697 m 416.909 667.594 l 410.012 660.874 m 416.909 667.771 l 410.012 661.055 m 416.909 667.953 l 410.012 661.236 m 416.909 668.133 l 410.012 661.418 m 416.909 668.315 l 410.012 661.595 m 416.909 668.492 l 410.012 661.776 m 416.909 668.673 l 410.012 661.957 m 416.909 668.855 l 410.012 662.139 m 416.909 669.036 l 410.012 662.316 m 416.909 669.213 l 410.012 662.496 m 416.909 669.394 l 410.012 662.678 m 416.909 669.575 l 410.012 662.855 m 416.909 669.752 l 410.012 663.036 m 416.909 669.933 l 410.012 663.217 m 416.909 670.114 l 410.012 663.399 m 416.909 670.296 l 410.012 663.575 m 416.909 670.472 l 410.012 663.756 m 416.909 670.654 l 410.012 663.938 m 416.909 670.835 l 410.012 664.119 m 416.909 671.017 l 410.012 664.296 m 416.909 671.193 l 410.012 664.478 m 416.909 671.375 l 410.012 664.659 m 416.909 671.556 l 410.012 664.836 m 416.909 671.733 l 410.012 665.016 m 416.909 671.914 l 410.012 665.198 m 416.909 672.095 l 410.012 665.379 m 416.909 672.276 l 410.012 665.556 m 416.909 672.453 l 410.012 665.737 m 416.909 672.635 l 410.012 665.919 m 416.909 672.816 l 410.012 666.1 m 416.909 672.997 l 410.012 666.277 m 416.909 673.174 l 410.012 666.458 m 416.909 673.356 l 410.012 666.64 m 416.909 673.536 l 410.012 666.821 m 416.909 673.718 l 410.012 666.998 m 416.909 673.895 l 410.012 667.179 m 416.909 674.076 l 410.012 667.36 m 416.909 674.257 l 410.012 667.537 m 416.909 674.434 l 410.012 667.718 m 416.909 674.616 l 410.012 667.9 m 416.909 674.796 l 410.012 668.081 m 416.909 674.978 l 410.012 668.257 m 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416.909 680.2 l 410.012 673.479 m 416.909 680.377 l 410.012 673.661 m 416.909 680.557 l 410.012 673.842 m 416.909 680.739 l 410.012 674.024 m 416.909 680.921 l 410.012 674.2 m 416.909 681.097 l 410.012 674.381 m 416.909 681.279 l 410.012 674.562 m 416.909 681.46 l 410.012 674.744 m 416.909 681.641 l 410.012 674.921 m 416.909 681.818 l 410.012 675.102 m 416.909 681.999 l 410.012 675.283 m 416.909 682.18 l 410.012 675.464 m 416.909 682.361 l 410.012 675.641 m 416.909 682.539 l 410.012 675.822 m 416.909 682.72 l 410.012 676.004 m 416.909 682.901 l 410.012 676.181 m 416.909 683.078 l 410.012 676.362 m 416.909 683.259 l 410.012 676.543 m 416.909 683.441 l 410.012 676.725 m 416.909 683.622 l 410.012 676.901 m 416.909 683.798 l 410.012 677.083 m 416.909 683.98 l 410.012 677.264 m 416.909 684.162 l 410.012 677.445 m 416.909 684.342 l 410.012 677.622 m 416.909 684.519 l 410.012 677.803 m 416.909 684.7 l 410.012 677.984 m 416.909 684.882 l 410.012 678.161 m 416.909 685.059 l 410.012 678.343 m 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410.012 688.428 m 416.378 694.795 l 410.012 688.609 m 416.197 694.795 l 410.012 688.786 m 416.02 694.795 l 410.012 688.967 m 415.839 694.795 l 410.012 689.148 m 415.658 694.795 l 410.012 689.33 m 415.476 694.795 l 410.012 689.506 m 415.299 694.795 l 410.012 689.688 m 415.118 694.795 l 410.012 689.869 m 414.936 694.795 l 410.012 690.05 m 414.756 694.795 l 410.012 690.227 m 414.579 694.795 l 410.012 690.409 m 414.398 694.795 l 410.012 690.59 m 414.216 694.795 l 410.012 690.771 m 414.039 694.795 l 410.012 690.948 m 413.858 694.795 l S 416.909 724.859 m 423.806 731.757 l 416.909 725.036 m 423.806 731.934 l 416.909 725.217 m 423.806 732.115 l 416.909 725.399 m 423.806 732.297 l 416.909 725.58 m 423.806 732.477 l 416.909 725.757 m 423.806 732.654 l 416.909 725.938 m 423.806 732.836 l 416.909 726.12 m 423.806 733.017 l 416.909 726.297 m 423.806 733.193 l 416.909 726.478 m 423.806 733.375 l 416.909 726.659 m 423.806 733.556 l 416.909 726.84 m 423.806 733.737 l 416.909 727.017 m 423.806 733.914 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m 423.806 660.264 l 416.909 653.547 m 423.806 660.445 l 416.909 653.729 m 423.806 660.626 l 416.909 653.906 m 423.806 660.803 l 416.909 654.087 m 423.806 660.984 l 416.909 654.268 m 423.806 661.166 l 416.909 654.445 m 423.806 661.342 l 416.909 654.627 m 423.806 661.524 l 416.909 654.808 m 423.806 661.705 l 416.909 654.989 m 423.806 661.886 l 416.909 655.166 m 423.806 662.064 l 416.909 655.348 m 423.806 662.245 l 416.909 655.528 m 423.806 662.426 l 416.909 655.71 m 423.806 662.607 l 416.909 655.886 m 423.806 662.784 l 416.909 656.068 m 423.806 662.965 l 416.909 656.25 m 423.806 663.147 l 416.909 656.426 m 423.806 663.323 l 416.909 656.607 m 423.806 663.504 l 416.909 656.789 m 423.806 663.686 l 416.909 656.97 m 423.806 663.867 l 416.909 657.147 m 423.806 664.044 l 416.909 657.328 m 423.806 664.225 l 416.909 657.509 m 423.806 664.406 l 416.909 657.691 m 423.806 664.588 l 416.909 657.868 m 423.806 664.765 l 416.909 658.048 m 423.806 664.946 l 416.909 658.23 m 423.806 665.128 l 416.909 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l 490.559 639.678 m 490.559 639.678 l 490.379 639.678 m 490.379 639.678 l 490.198 639.678 m 490.198 639.678 l 490.015 639.678 m 490.015 639.678 l 489.84 639.678 m 489.84 639.678 l 489.657 639.678 m 489.657 639.678 l 489.477 639.678 m 489.477 639.678 l 489.301 639.678 m 489.301 639.678 l 489.118 639.678 m 489.118 639.678 l 488.937 639.678 m 488.937 639.678 l 488.756 639.678 m 488.756 639.678 l 488.578 639.678 m 488.578 639.678 l 488.398 639.678 m 488.398 639.678 l 488.216 639.678 m 488.216 639.678 l 488.035 639.678 m 488.035 639.678 l 487.858 639.678 m 487.858 639.678 l 487.676 639.678 m 487.676 639.678 l 487.496 639.678 m 487.496 639.678 l 487.318 639.678 m 487.318 639.678 l 487.138 639.678 m 487.138 639.678 l 486.956 639.678 m 486.956 639.678 l 486.775 639.678 m 486.775 639.678 l 486.598 639.678 m 486.598 639.678 l 486.417 639.678 m 486.417 639.678 l 486.235 639.678 m 486.235 639.678 l 486.054 639.678 m 486.054 639.678 l 485.877 639.678 m 485.877 639.678 l 485.696 639.678 m 485.696 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m 552.683 639.678 l 552.507 639.678 m 552.507 639.678 l 552.326 639.678 m 552.326 639.678 l 552.145 639.678 m 552.145 639.678 l 551.963 639.678 m 551.963 639.678 l 551.786 639.678 m 551.786 639.678 l 551.605 639.678 m 551.605 639.678 l 551.424 639.678 m 551.424 639.678 l 551.242 639.678 m 551.242 639.678 l 551.066 639.678 m 551.066 639.678 l 550.884 639.678 m 550.884 639.678 l 550.704 639.678 m 550.704 639.678 l 550.525 639.678 m 550.525 639.678 l 550.344 639.678 m 550.344 639.678 l 550.165 639.678 m 550.165 639.678 l 549.982 639.678 m 549.982 639.678 l 549.806 639.678 m 549.806 639.678 l 549.625 639.678 m 549.625 639.678 l 549.443 639.678 m 549.443 639.678 l 549.261 639.678 m 549.261 639.678 l 549.085 639.678 m 549.085 639.678 l 548.903 639.678 m 548.903 639.678 l 548.722 639.678 m 548.722 639.678 l 548.541 639.678 m 548.541 639.678 l 548.365 639.678 m 548.365 639.678 l 548.182 639.678 m 548.182 639.678 l 548.002 639.678 m 548.002 639.678 l 547.825 639.678 m 547.825 639.678 l 547.643 639.678 m 547.643 639.678 l 547.463 639.678 m 547.463 639.678 l 547.281 639.678 m 547.281 639.678 l 547.104 639.678 m 547.104 639.678 l 546.923 639.678 m 546.923 639.678 l 546.742 639.678 m 546.742 639.678 l 546.56 639.678 m 546.56 639.678 l 546.384 639.678 m 546.384 639.678 l 546.202 639.678 m 546.202 639.678 l 546.021 639.678 m 546.021 639.678 l 545.844 639.678 m 545.844 639.678 l 545.663 639.678 m 545.663 639.678 l 545.481 639.678 m 545.481 639.678 l 545.3 639.678 m 545.3 639.678 l 545.124 639.678 m 545.124 639.678 l 544.941 639.678 m 544.941 639.678 l 544.76 639.678 m 544.76 639.678 l 544.58 639.678 m 544.58 639.678 l 544.403 639.678 m 544.403 639.678 l 544.221 639.678 m 544.221 639.678 l 544.041 639.678 m 544.041 639.678 l 543.863 639.678 m 543.863 639.678 l 543.682 639.678 m 543.682 639.678 l 543.5 639.678 m 543.5 639.678 l 543.319 639.678 m 543.319 639.678 l 543.142 639.678 m 543.142 639.678 l 542.961 639.678 m 542.961 639.678 l 542.781 639.678 m 542.781 639.678 l 542.599 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537.558 639.678 l 537.377 639.678 m 537.377 639.678 l 537.2 639.678 m 537.2 639.678 l 537.02 639.678 m 537.02 639.678 l 536.838 639.678 m 536.838 639.678 l 536.657 639.678 m 536.657 639.678 l 536.479 639.678 m 536.479 639.678 l 536.299 639.678 m 536.299 639.678 l 536.117 639.678 m 536.117 639.678 l 535.935 639.678 m 535.935 639.678 l 535.759 639.678 m 535.759 639.678 l 535.578 639.678 m 535.578 639.678 l 535.397 639.678 m 535.397 639.678 l 535.219 639.678 m 535.219 639.678 l 535.038 639.678 m 535.038 639.678 l 534.856 639.678 m 534.856 639.678 l 534.676 639.678 m 534.676 639.678 l 534.499 639.678 m 534.499 639.678 l 534.318 639.678 m 534.318 639.678 l 534.135 639.678 m 534.135 639.678 l 533.955 639.678 m 533.955 639.678 l 533.778 639.678 m 533.778 639.678 l 533.596 639.678 m 533.596 639.678 l 533.415 639.678 m 533.415 639.678 l 533.238 639.678 m 533.238 639.678 l 533.058 639.678 m 533.058 639.678 l 532.877 639.678 m 532.877 639.678 l 532.695 639.678 m 532.695 639.678 l 532.518 639.678 m 532.518 639.678 l 532.338 639.678 m 532.338 639.678 l 532.155 639.678 m 532.155 639.678 l 531.974 639.678 m 531.974 639.678 l 531.797 639.678 m 531.797 639.678 l 531.616 639.678 m 531.616 639.678 l 531.435 639.678 m 531.435 639.678 l 531.254 639.678 m 531.254 639.678 l 531.077 639.678 m 531.077 639.678 l 530.896 639.678 m 530.896 639.678 l 530.715 639.678 m 530.715 639.678 l 530.538 639.678 m 530.538 639.678 l 530.356 639.678 m 530.356 639.678 l 530.175 639.678 m 530.175 639.678 l 529.994 639.678 m 529.994 639.678 l 529.816 639.678 m 529.816 639.678 l 529.635 639.678 m 529.635 639.678 l 529.453 639.678 m 529.453 639.678 l 529.273 639.678 m 529.273 639.678 l 529.096 639.678 m 529.096 639.678 l 528.915 639.678 m 528.915 639.678 l 528.733 639.678 m 528.733 639.678 l 528.556 639.678 m 528.556 639.678 l 528.376 639.678 m 528.376 639.678 l 528.194 639.678 m 528.194 639.678 l 528.012 639.678 m 528.012 639.678 l 527.836 639.678 m 527.836 639.678 l 527.656 639.678 m 527.656 639.678 l 527.473 639.678 m 527.473 639.678 l 527.293 639.678 m 527.293 639.678 l 527.114 639.678 m 527.114 639.678 l 526.934 639.678 m 526.934 639.678 l 526.753 639.678 m 526.753 639.678 l 526.576 639.678 m 526.576 639.678 l 526.394 639.678 m 526.394 639.678 l 526.213 639.678 m 526.213 639.678 l 526.032 639.678 m 526.032 639.678 l 525.855 639.678 m 525.855 639.678 l 525.675 639.678 m 525.675 639.678 l 525.492 639.678 m 525.492 639.678 l 525.312 639.678 m 525.312 639.678 l 525.134 639.678 m 525.134 639.678 l 524.954 639.678 m 524.954 639.678 l 524.771 639.678 m 524.771 639.678 l 524.591 639.678 m 524.591 639.678 l 524.414 639.678 m 524.414 639.678 l 524.232 639.678 m 524.232 639.678 l 524.052 639.678 m 524.052 639.678 l 523.875 639.678 m 523.875 639.678 l 523.693 639.678 m 523.693 639.678 l 523.512 639.678 m 523.512 639.678 l 523.331 639.678 m 523.331 639.678 l 523.153 639.678 m 523.153 639.678 l 522.973 639.678 m 522.973 639.678 l 522.791 639.678 m 522.791 639.678 l 522.61 639.678 m 522.61 639.678 l 522.432 639.678 m 522.432 639.678 l 522.252 639.678 m 522.252 639.678 l 522.07 639.678 m 522.07 639.678 l 521.893 639.678 m 521.893 639.678 l 521.713 639.678 m 521.713 639.678 l 521.531 639.678 m 521.531 639.678 l 521.35 639.678 m 521.35 639.678 l 521.174 639.678 m 521.174 639.678 l 520.992 639.678 m 520.992 639.678 l 520.81 639.678 m 520.81 639.678 l 520.63 639.678 m 520.63 639.678 l 520.452 639.678 m 520.452 639.678 l 520.271 639.678 m 520.271 639.678 l 520.09 639.678 m 520.09 639.678 l 519.913 639.678 m 519.913 639.678 l 519.731 639.678 m 519.731 639.678 l 519.551 639.678 m 519.551 639.678 l 519.369 639.678 m 519.369 639.678 l 519.191 639.678 m 519.191 639.678 l 519.01 639.678 m 519.01 639.678 l 518.83 639.678 m 518.83 639.678 l 518.648 639.678 m 518.648 639.678 l 518.471 639.678 m 518.471 639.678 l 518.291 639.678 m 518.291 639.678 l 518.108 639.678 m 518.108 639.678 l 517.932 639.678 m 517.932 639.678 l 517.751 639.678 m 517.751 639.678 l 517.569 639.678 m 517.569 639.678 l 517.388 639.678 m 517.388 639.678 l 517.212 639.678 m 517.212 639.678 l 517.03 639.678 m 517.03 639.678 l S 547.957 639.678 m 554.854 639.678 l 547.957 639.678 l 541.059 639.678 m 547.957 639.678 l 541.059 639.678 l 534.163 639.678 m 541.059 639.678 l 534.163 639.678 l 527.265 639.678 m 534.163 639.678 l 527.265 639.678 l 520.369 639.678 m 527.265 639.678 l 520.369 639.678 l 513.471 639.678 m 520.369 639.678 l 513.471 639.678 l 506.574 639.678 m 513.471 639.678 l 506.574 639.678 l 499.676 639.678 m 506.574 639.678 l 499.676 639.678 l 492.778 639.678 m 499.676 639.678 l 492.778 639.678 l 485.882 639.678 m 492.778 639.678 l 485.882 639.678 l 478.984 639.678 m 485.882 639.678 l 478.984 639.678 l 472.087 639.678 m 478.984 639.678 l 472.087 639.678 l 465.19 639.678 6.897 0.027 re 458.293 639.678 6.897 0.067 re 451.396 639.678 6.897 0.137 re 444.499 639.678 6.897 0.421 re 437.601 639.678 6.898 2.909 re 430.703 639.678 6.898 12.415 re 423.806 639.678 6.897 50.727 re 416.909 639.678 6.897 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503.522 m 554.363 503.522 l S BT /T1_4 1 Tf 5.128 Tc 6.6319 0 0 6.632 345.602 489.1975 Tm [(0)-278(1)5128(02)5128(03)5128(04)-667(5)5128(0)]TJ ET 347.444 593.872 m 343.466 593.872 l 347.444 563.755 m 343.466 563.755 l 347.444 533.64 m 343.466 533.64 l 347.444 503.522 m 343.466 503.522 l 347.444 503.522 m 347.444 593.872 l S BT /T1_4 1 Tf 0 Tc 0 6.632 -6.6319 0 337.8148 501.6795 Tm [(0)-3290(0.05)-2873(0.1)-2873(0.15)]TJ ET q 347.444 503.522 206.919 102.664 re W n 347.444 503.522 m 347.444 606.186 l S 0 0 0 0.202 K 375.034 504.46 m 381.931 511.356 l 375.034 504.641 m 381.931 511.538 l 375.034 504.823 m 381.931 511.719 l 375.034 505 m 381.931 511.896 l 375.034 505.179 m 381.931 512.078 l 375.034 505.361 m 381.869 512.196 l 375.034 505.539 m 381.688 512.196 l 375.034 505.719 m 381.511 512.196 l 375.034 505.901 m 381.33 512.196 l 375.034 506.082 m 381.148 512.196 l 375.034 506.259 m 380.967 512.196 l 375.034 506.44 m 380.79 512.196 l 375.034 506.622 m 380.609 512.196 l 375.034 506.802 m 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350.867 503.522 m 350.867 503.522 l 350.685 503.522 m 350.685 503.522 l 350.504 503.522 m 350.504 503.522 l 350.327 503.522 m 350.327 503.522 l 350.146 503.522 m 350.146 503.522 l 349.965 503.522 m 349.965 503.522 l 349.783 503.522 m 349.783 503.522 l 349.606 503.522 m 349.606 503.522 l 349.425 503.522 m 349.425 503.522 l 349.244 503.522 m 349.244 503.522 l 349.067 503.522 m 349.067 503.522 l 348.886 503.522 m 348.886 503.522 l 348.704 503.522 m 348.704 503.522 l 348.524 503.522 m 348.524 503.522 l 348.347 503.522 m 348.347 503.522 l 348.165 503.522 m 348.165 503.522 l 347.984 503.522 m 347.984 503.522 l 347.803 503.522 m 347.803 503.522 l 347.626 503.522 m 347.626 503.522 l S 382.02 503.522 m 388.828 510.331 l 381.931 503.614 m 388.828 510.512 l 381.931 503.793 m 388.828 510.689 l 381.931 503.973 m 388.828 510.87 l 381.931 504.155 m 388.828 511.052 l 381.931 504.336 m 388.828 511.233 l 381.931 504.512 m 388.828 511.411 l 381.931 504.694 m 388.828 511.591 l 381.931 504.876 m 388.828 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520 m 388.828 526.899 l 381.931 520.182 m 388.828 527.079 l 381.931 520.362 m 388.828 527.259 l 381.931 520.541 m 388.828 527.437 l 381.931 520.721 m 388.828 527.618 l 381.931 520.903 m 388.828 527.799 l 381.931 521.08 m 388.828 527.976 l 381.931 521.26 m 388.828 528.158 l 381.931 521.442 m 388.828 528.339 l 381.931 521.624 m 388.828 528.521 l 381.931 521.799 m 388.828 528.697 l 381.931 521.982 m 388.828 528.879 l 381.931 522.163 m 388.828 529.059 l 381.931 522.343 m 388.828 529.242 l 381.931 522.521 m 388.828 529.418 l 381.931 522.701 m 388.828 529.599 l 381.931 522.883 m 388.828 529.781 l 381.931 523.06 m 388.828 529.957 l 381.931 523.242 m 388.828 530.139 l 381.931 523.422 m 388.828 530.32 l 381.931 523.604 m 388.828 530.502 l 381.931 523.781 m 388.828 530.678 l 381.931 523.963 m 388.828 530.859 l 381.931 524.143 m 388.828 531.04 l 381.931 524.325 m 388.828 531.222 l 381.931 524.502 m 388.828 531.398 l 381.931 524.682 m 388.828 531.581 l 381.931 524.865 m 388.709 531.637 l 381.931 525.04 m 388.527 531.637 l 381.931 525.222 m 388.346 531.637 l 381.931 525.403 m 388.165 531.637 l 381.931 525.585 m 387.989 531.637 l 381.931 525.761 m 387.807 531.637 l 381.931 525.943 m 387.625 531.637 l 381.931 526.125 m 387.449 531.637 l 381.931 526.306 m 387.268 531.637 l 381.931 526.482 m 387.086 531.637 l 381.931 526.664 m 386.905 531.637 l 381.931 526.844 m 386.728 531.637 l 381.931 527.025 m 386.547 531.637 l 381.931 527.203 m 386.365 531.637 l 381.931 527.383 m 386.184 531.637 l 381.931 527.566 m 386.007 531.637 l 381.931 527.742 m 385.827 531.637 l 381.931 527.923 m 385.645 531.637 l 381.931 528.105 m 385.468 531.637 l 381.931 528.286 m 385.287 531.637 l 381.931 528.463 m 385.105 531.637 l 381.931 528.645 m 384.924 531.637 l 381.931 528.825 m 384.747 531.637 l 381.931 529.007 m 384.566 531.637 l 381.931 529.183 m 384.384 531.637 l 381.931 529.365 m 384.204 531.637 l 381.931 529.546 m 384.027 531.637 l 381.931 529.722 m 383.845 531.637 l 381.931 529.905 m 383.664 531.637 l 381.931 530.086 m 383.483 531.637 l 381.931 530.267 m 383.306 531.637 l 381.931 530.444 m 383.125 531.637 l 381.931 530.625 m 382.943 531.637 l 381.931 530.806 m 382.767 531.637 l 381.931 530.988 m 382.585 531.637 l 381.931 531.164 m 382.404 531.637 l 381.931 531.346 m 382.223 531.637 l 381.931 531.527 m 382.045 531.637 l 381.838 503.522 m 381.931 503.614 l 381.661 503.522 m 381.931 503.793 l 381.48 503.522 m 381.931 503.973 l 381.299 503.522 m 381.931 504.155 l 381.118 503.522 m 381.931 504.336 l 380.94 503.522 m 381.931 504.512 l 380.759 503.522 m 381.931 504.694 l 380.578 503.522 m 381.931 504.876 l 380.396 503.522 m 381.931 505.055 l 380.22 503.522 m 381.931 505.234 l 380.039 503.522 m 381.931 505.415 l 379.857 503.522 m 381.931 505.596 l 379.681 503.522 m 381.931 505.772 l 379.499 503.522 m 381.931 505.953 l 379.318 503.522 m 381.931 506.135 l 379.137 503.522 m 381.931 506.316 l 378.96 503.522 m 381.931 506.494 l 378.779 503.522 m 381.931 506.674 l 378.597 503.522 m 381.931 506.856 l 378.415 503.522 m 381.931 507.038 l 378.239 503.522 m 381.931 507.214 l 378.058 503.522 m 381.931 507.395 l 377.876 503.522 m 381.931 507.577 l 377.7 503.522 m 381.931 507.754 l 377.518 503.522 m 381.931 507.935 l 377.337 503.522 m 381.931 508.116 l 377.156 503.522 m 381.931 508.296 l 376.979 503.522 m 381.931 508.474 l 376.798 503.522 m 381.931 508.655 l 376.617 503.522 m 381.931 508.837 l 376.435 503.522 m 381.931 509.018 l 376.258 503.522 m 381.931 509.195 l 376.077 503.522 m 381.931 509.377 l 375.896 503.522 m 381.931 509.557 l 375.719 503.522 m 381.931 509.734 l 375.538 503.522 m 381.931 509.916 l 375.356 503.522 m 381.931 510.096 l 375.175 503.522 m 381.931 510.278 l 375.034 503.558 m 381.931 510.455 l 375.034 503.738 m 381.931 510.635 l 375.034 503.921 m 381.931 510.818 l 375.034 504.101 m 381.931 510.999 l 375.034 504.278 m 381.931 511.176 l S 388.828 522.755 m 395.726 529.653 l 388.828 522.936 m 395.726 529.834 l 388.828 523.118 m 395.726 530.015 l 388.828 523.294 m 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533.379 m 395.726 540.277 l 388.828 533.561 m 395.726 540.459 l 388.828 533.742 m 395.726 540.638 l 388.828 533.924 m 395.726 540.821 l 388.828 534.1 m 395.726 540.997 l 388.828 534.282 m 395.726 541.178 l 388.828 534.463 m 395.726 541.36 l 388.828 534.639 m 395.726 541.537 l 388.828 534.821 m 395.726 541.718 l 388.828 535.002 m 395.726 541.899 l 388.828 535.183 m 395.726 542.081 l 388.828 535.36 m 395.726 542.257 l 388.828 535.542 m 395.726 542.439 l 388.828 535.722 m 395.726 542.621 l 388.828 535.905 m 395.726 542.801 l 388.828 536.081 m 395.726 542.977 l 388.828 536.263 m 395.726 543.16 l 388.828 536.443 m 395.726 543.34 l 388.828 536.621 m 395.726 543.518 l 388.828 536.802 m 395.726 543.699 l 388.828 536.982 m 395.726 543.88 l 388.828 537.164 m 395.726 544.062 l 388.828 537.34 m 395.726 544.239 l 388.828 537.522 m 395.726 544.42 l 388.828 537.704 m 395.726 544.6 l 388.828 537.884 m 395.726 544.782 l 388.828 538.061 m 395.726 544.959 l 388.828 538.244 m 395.726 545.14 l 388.828 538.424 m 395.726 545.321 l 388.828 538.602 m 395.726 545.499 l 388.828 538.782 m 395.726 545.679 l 388.828 538.963 m 395.726 545.861 l 388.828 539.145 m 395.726 546.043 l 388.828 539.322 m 395.726 546.219 l 388.828 539.503 m 395.726 546.401 l 388.828 539.684 m 395.726 546.582 l 388.828 539.866 m 395.726 546.762 l 388.828 540.043 m 395.726 546.939 l 388.828 540.223 m 395.726 547.121 l 388.828 540.404 m 395.726 547.302 l 388.828 540.583 m 395.726 547.479 l 388.828 540.763 m 395.726 547.66 l 388.828 540.945 m 395.726 547.842 l 388.828 541.126 m 395.726 548.023 l 388.828 541.302 m 395.726 548.2 l 388.828 541.484 m 395.726 548.381 l 388.828 541.665 m 395.726 548.562 l 388.828 541.846 m 395.726 548.744 l 388.828 542.023 m 395.726 548.921 l 388.828 542.205 m 395.726 549.101 l 388.828 542.386 m 395.726 549.283 l 388.828 542.567 m 395.726 549.464 l 388.828 542.743 m 395.726 549.641 l 388.828 542.925 m 395.726 549.823 l 388.828 543.106 m 395.726 550.003 l 388.828 543.284 m 395.726 550.181 l 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516.56 l 395.726 509.845 m 402.622 516.742 l 395.726 510.026 m 402.622 516.923 l 395.726 510.207 m 402.622 517.104 l 395.726 510.385 m 402.622 517.282 l 395.726 510.565 m 402.622 517.463 l 395.726 510.746 m 402.622 517.645 l 395.726 510.923 m 402.622 517.821 l 395.726 511.104 m 402.622 518.003 l 395.726 511.287 m 402.622 518.183 l 395.726 511.466 m 402.622 518.364 l 395.726 511.644 m 402.622 518.542 l 395.726 511.826 m 402.622 518.722 l 395.726 512.007 m 402.622 518.904 l 395.726 512.188 m 402.622 519.086 l S 409.52 538.588 m 411.032 540.095 l 409.52 538.764 m 410.851 540.095 l 409.52 538.947 m 410.669 540.095 l 409.52 539.128 m 410.488 540.095 l 409.52 539.309 m 410.311 540.095 l 409.52 539.485 m 410.13 540.095 l 409.52 539.667 m 409.949 540.095 l 409.52 539.847 m 409.768 540.095 l 409.52 540.025 m 409.591 540.095 l 409.392 503.522 m 409.52 503.65 l 409.21 503.522 m 409.52 503.832 l 409.029 503.522 m 409.52 504.013 l 408.852 503.522 m 409.52 504.189 l 408.671 503.522 m 409.52 504.372 l 408.49 503.522 m 409.52 504.552 l 408.312 503.522 m 409.52 504.729 l 408.132 503.522 m 409.52 504.911 l 407.951 503.522 m 409.52 505.091 l 407.769 503.522 m 409.52 505.273 l 407.592 503.522 m 409.52 505.451 l 407.411 503.522 m 409.52 505.63 l 407.23 503.522 m 409.52 505.813 l 407.049 503.522 m 409.52 505.994 l 406.872 503.522 m 409.52 506.171 l 406.69 503.522 m 409.52 506.352 l 406.509 503.522 m 409.52 506.533 l 406.328 503.522 m 409.52 506.714 l 406.151 503.522 m 409.52 506.891 l 405.97 503.522 m 409.52 507.072 l 405.789 503.522 m 409.52 507.254 l 405.612 503.522 m 409.52 507.43 l 405.431 503.522 m 409.52 507.612 l 405.249 503.522 m 409.52 507.794 l 405.068 503.522 m 409.52 507.974 l 404.891 503.522 m 409.52 508.152 l 404.71 503.522 m 409.52 508.333 l 404.528 503.522 m 409.52 508.514 l 404.347 503.522 m 409.52 508.695 l 404.17 503.522 m 409.52 508.872 l 403.989 503.522 m 409.52 509.053 l 403.808 503.522 m 409.52 509.234 l 403.631 503.522 m 409.52 509.411 l 403.45 503.522 m 409.52 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518.364 m 409.52 525.262 l 402.622 518.543 m 409.52 525.439 l 402.622 518.722 m 409.52 525.62 l 402.622 518.904 m 409.52 525.801 l 402.622 519.086 m 409.52 525.982 l 402.622 519.262 m 409.52 526.16 l 402.622 519.443 m 409.52 526.34 l 402.622 519.626 m 409.52 526.522 l 402.622 519.801 m 409.52 526.698 l 402.622 519.984 m 409.52 526.88 l 402.622 520.165 m 409.52 527.061 l 402.622 520.345 m 409.52 527.243 l 402.622 520.522 m 409.52 527.42 l 402.622 520.703 m 409.52 527.601 l 402.622 520.885 m 409.52 527.783 l 402.622 521.066 m 409.52 527.963 l 402.622 521.243 m 409.52 528.14 l 402.622 521.424 m 409.52 528.321 l 402.622 521.606 m 409.52 528.503 l 402.622 521.782 m 409.52 528.679 l 402.622 521.964 m 409.52 528.861 l 402.622 522.144 m 409.52 529.042 l 402.622 522.327 m 409.52 529.224 l 402.622 522.504 m 409.52 529.4 l 402.622 522.684 m 409.52 529.582 l 402.622 522.866 m 409.52 529.763 l 402.622 523.046 m 409.52 529.944 l 402.622 523.224 m 409.52 530.122 l 402.622 523.405 m 409.52 530.302 l 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m 416.417 522.433 l 409.52 515.716 m 416.417 522.614 l 409.52 515.898 m 416.417 522.795 l 409.52 516.075 m 416.417 522.972 l 409.52 516.255 m 416.417 523.153 l 409.52 516.436 m 416.417 523.335 l 409.52 516.618 m 416.417 523.515 l 409.52 516.795 m 416.417 523.692 l 409.52 516.977 m 416.417 523.874 l 409.52 517.158 m 416.417 524.055 l 409.52 517.338 m 416.417 524.236 l 409.52 517.516 m 416.417 524.414 l 409.52 517.697 m 416.417 524.593 l 409.52 517.879 m 416.417 524.776 l 409.52 518.055 m 416.417 524.952 l 409.52 518.237 m 416.417 525.133 l 409.52 518.419 m 416.417 525.315 l 409.52 518.599 m 416.417 525.497 l 409.52 518.775 m 416.417 525.673 l 409.52 518.957 m 416.417 525.854 l 409.52 519.138 m 416.417 526.036 l 409.52 519.32 m 416.417 526.216 l 409.52 519.497 m 416.417 526.394 l 409.52 519.677 m 416.417 526.575 l 409.52 519.86 m 416.417 526.756 l 409.52 520.036 m 416.417 526.932 l 409.52 520.216 m 416.417 527.115 l 409.52 520.398 m 416.417 527.295 l 409.52 520.58 m 416.417 527.477 l 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532.699 l 409.52 525.982 m 416.417 532.88 l 409.52 526.16 m 416.417 533.056 l 409.52 526.34 m 416.417 533.238 l 409.52 526.522 m 416.417 533.42 l 409.52 526.698 m 416.417 533.595 l 409.52 526.88 m 416.417 533.778 l 409.52 527.061 m 416.417 533.958 l 409.52 527.243 m 416.417 534.14 l 409.52 527.42 m 416.417 534.317 l 409.52 527.601 m 416.417 534.499 l 409.52 527.783 m 416.417 534.679 l 409.52 527.963 m 416.417 534.861 l 409.52 528.14 m 416.417 535.038 l 409.52 528.321 m 416.417 535.219 l 409.52 528.503 m 416.417 535.4 l 409.52 528.679 m 416.417 535.577 l 409.52 528.861 m 416.417 535.758 l 409.52 529.042 m 416.417 535.939 l 409.52 529.224 m 416.417 536.121 l 409.52 529.4 m 416.417 536.296 l 409.52 529.582 m 416.417 536.479 l 409.52 529.763 m 416.417 536.66 l 409.52 529.944 m 416.417 536.841 l 409.52 530.122 m 416.417 537.018 l 409.52 530.302 m 416.417 537.2 l 409.52 530.483 m 416.417 537.381 l 409.52 530.665 m 416.417 537.563 l 409.52 530.841 m 416.417 537.739 l 409.52 531.023 m 416.417 537.92 l 409.52 531.205 m 416.417 538.101 l 409.52 531.38 m 416.417 538.278 l 409.52 531.563 m 416.417 538.46 l 409.52 531.744 m 416.417 538.64 l 409.52 531.924 m 416.417 538.823 l 409.52 532.102 m 416.417 538.999 l 409.52 532.283 m 416.417 539.18 l 409.52 532.464 m 416.417 539.362 l 409.52 532.646 m 416.417 539.543 l 409.52 532.822 m 416.417 539.72 l 409.52 533.004 m 416.417 539.902 l 409.52 533.185 m 416.417 540.082 l 409.52 533.362 m 416.254 540.095 l 409.52 533.544 m 416.073 540.095 l 409.52 533.724 m 415.891 540.095 l 409.52 533.906 m 415.709 540.095 l 409.52 534.082 m 415.533 540.095 l 409.52 534.263 m 415.351 540.095 l 409.52 534.445 m 415.17 540.095 l 409.52 534.627 m 414.993 540.095 l 409.52 534.803 m 414.812 540.095 l 409.52 534.985 m 414.631 540.095 l 409.52 535.166 m 414.45 540.095 l 409.52 535.342 m 414.273 540.095 l 409.52 535.524 m 414.092 540.095 l 409.52 535.705 m 413.911 540.095 l 409.52 535.886 m 413.729 540.095 l 409.52 536.063 m 413.552 540.095 l 409.52 536.245 m 413.371 540.095 l 409.52 536.425 m 413.19 540.095 l 409.52 536.607 m 413.013 540.095 l 409.52 536.784 m 412.831 540.095 l 409.52 536.965 m 412.65 540.095 l 409.52 537.146 m 412.469 540.095 l 409.52 537.324 m 412.292 540.095 l 409.52 537.505 m 412.111 540.095 l 409.52 537.686 m 411.93 540.095 l 409.52 537.868 m 411.748 540.095 l 409.52 538.044 m 411.572 540.095 l 409.52 538.225 m 411.39 540.095 l 409.52 538.406 m 411.209 540.095 l S 416.417 504.963 m 423.315 511.861 l 416.417 505.145 m 423.315 512.042 l 416.417 505.326 m 423.315 512.223 l 416.417 505.506 m 423.315 512.405 l 416.417 505.685 m 423.315 512.582 l 416.417 505.865 m 423.315 512.762 l 416.417 506.047 m 423.315 512.945 l 416.417 506.228 m 423.315 513.125 l 416.417 506.405 m 423.315 513.303 l 416.417 506.587 m 423.315 513.484 l 416.417 506.767 m 423.315 513.665 l 416.417 506.949 m 423.315 513.846 l 416.417 507.126 m 423.315 514.023 l 416.417 507.307 m 423.315 514.204 l 416.417 507.488 m 423.315 514.385 l 416.417 507.665 m 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522.795 m 423.315 529.692 l 416.417 522.972 m 423.315 529.869 l 416.417 523.153 m 423.315 530.05 l 416.417 523.335 m 423.315 530.232 l 416.417 523.515 m 423.315 530.414 l 416.417 523.692 m 423.315 530.588 l 416.417 523.874 m 423.315 530.771 l 416.417 524.055 m 423.315 530.952 l 416.417 524.236 m 423.315 531.133 l 416.417 524.414 m 423.315 531.31 l 416.417 524.593 m 423.315 531.491 l 416.417 524.776 m 423.315 531.673 l 416.417 524.952 m 423.315 531.849 l 416.417 525.133 m 423.315 532.032 l 416.417 525.315 m 423.315 532.213 l 416.417 525.497 m 423.315 532.393 l 416.417 525.673 m 423.315 532.571 l 416.417 525.854 m 423.315 532.753 l 416.417 526.036 m 423.315 532.932 l 416.417 526.216 m 423.315 533.115 l 416.417 526.394 m 423.315 533.291 l 416.417 526.575 m 423.315 533.472 l 416.417 526.756 m 423.315 533.654 l 416.417 526.932 m 423.315 533.83 l 416.417 527.115 m 423.315 534.012 l 416.417 527.295 m 423.315 534.193 l 416.417 527.477 m 423.315 534.375 l 416.417 527.654 m 423.315 534.551 l 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535.038 l 416.417 532.88 m 418.575 535.038 l 416.417 533.056 m 418.394 535.038 l 416.417 533.238 m 418.217 535.038 l 416.417 533.42 m 418.036 535.038 l 416.417 533.595 m 417.855 535.038 l 416.417 533.778 m 417.678 535.038 l 416.417 533.958 m 417.496 535.038 l 416.417 534.14 m 417.315 535.038 l 416.417 534.317 m 417.134 535.038 l 416.417 534.499 m 416.957 535.038 l 416.417 534.679 m 416.775 535.038 l 416.417 534.861 m 416.594 535.038 l 416.413 503.522 m 416.417 503.526 l 416.236 503.522 m 416.417 503.705 l 416.055 503.522 m 416.417 503.884 l 415.873 503.522 m 416.417 504.066 l 415.692 503.522 m 416.417 504.248 l 415.515 503.522 m 416.417 504.423 l 415.334 503.522 m 416.417 504.606 l 415.153 503.522 m 416.417 504.787 l 414.976 503.522 m 416.417 504.963 l 414.795 503.522 m 416.417 505.145 l 414.613 503.522 m 416.417 505.326 l 414.432 503.522 m 416.417 505.506 l 414.255 503.522 m 416.417 505.685 l 414.074 503.522 m 416.417 505.865 l 413.893 503.522 m 416.417 506.047 l 413.711 503.522 m 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m 442.181 518.122 l 437.11 513.231 m 441.999 518.122 l 437.11 513.414 m 441.818 518.122 l 437.11 513.594 m 441.641 518.122 l 437.11 513.771 m 441.46 518.122 l 437.11 513.952 m 441.279 518.122 l 437.11 514.133 m 441.097 518.122 l 437.11 514.314 m 440.921 518.122 l 437.11 514.493 m 440.739 518.122 l 437.11 514.672 m 440.558 518.122 l 437.11 514.854 m 440.382 518.122 l 437.11 515.031 m 440.2 518.122 l 437.11 515.212 m 440.018 518.122 l 437.11 515.394 m 439.838 518.122 l 437.11 515.574 m 439.66 518.122 l 437.11 515.753 m 439.479 518.122 l 437.11 515.933 m 439.298 518.122 l 437.11 516.115 m 439.116 518.122 l 437.11 516.295 m 438.94 518.122 l 437.11 516.472 m 438.759 518.122 l 437.11 516.653 m 438.577 518.122 l 437.11 516.836 m 438.4 518.122 l 437.11 517.011 m 438.219 518.122 l 437.11 517.193 m 438.038 518.122 l 437.11 517.375 m 437.857 518.122 l 437.11 517.555 m 437.679 518.122 l 437.11 517.733 m 437.499 518.122 l 437.11 517.913 m 437.317 518.122 l 437.11 518.095 m 437.135 518.122 l 436.942 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-12.133 re 444.007 515.655 6.897 -12.133 re 437.11 515.906 6.897 -12.384 re 430.212 523.489 6.898 -19.967 re 423.315 525.257 6.897 -21.735 re 416.417 521.973 6.898 -18.451 re 409.52 522.224 6.897 -18.702 re 402.622 525.509 6.898 -21.987 re 395.726 530.815 6.897 -27.293 re 388.828 533.092 6.897 -29.57 re 381.931 528.795 6.898 -25.273 re 375.034 528.291 6.897 -24.769 re 368.137 514.893 6.897 -11.371 re 361.239 507.06 6.897 -3.538 re 354.342 503.522 m 361.239 503.522 l 354.342 503.522 l h 347.444 503.522 m 354.342 503.522 l 347.444 503.522 l h S Q BT /T1_5 1 Tf 10.9999 0 0 11 442.4291 474.9036 Tm (R)Tj /T1_4 1 Tf 0 11 -10.9999 0 326.3744 568.1655 Tm (Probability Density)Tj 0.0001 Tw 6.6319 0 0 6.632 419.8471 552.3925 Tm (Median Fixed = 14.7)Tj 0 Tw 4.068 -4.54 Td (Median Variable = 18.3)Tj 11.9999 0 0 12 332.4911 604.6426 Tm (B)Tj 0 0 0 1 k 8 0 0 8 450.4442 473.4546 Tm (o)Tj ET EMC /GS0 gs BT /T1_7 1 Tf 7 0 0 7 314.1761 455.8835 Tm [(Fig.)-194(2.)]TJ /T1_8 1 Tf 3.89 0 Td [(Effects)-194(of)-194(prior)-194(knowledge)-194(on)-194(uncertainty)-194(in)-194(the)-194(disease)-194(transmission)]TJ -3.89 -1.286 Td (rate)Tj /T1_9 1 Tf 2.069 0 Td (R)Tj /T1_8 1 Tf 5 0 0 5 332.9334 445.8835 Tm (0)Tj 7 0 0 7 335.7138 446.8835 Tm [(.)-179(We)-179(distinguish)-179(between)-179(epidemics)-179(in)-179(Old)-179(World)-179(populations)-179(and)-179(New)]TJ -3.077 -1.286 Td [(World)-281(populations)-281(because)-281(epidemics)-281(were)-281(more)-281(severe)-281(in)-281(New)-281(World)-281(pop-)]TJ 0 -1.286 TD [(ulations,)-336(apparently)-336(because)-336(of)-336(differences)-336(in)-336(previous)-336(exposure)-336(and)-336(social)]TJ T* [(structure)-280(\(15\).)-280(Because)-280(it)-280(is)-280(not)-280(clear)-280(which)-280(group)-280(is)-280(more)-280(similar)-280(to)-280(contem-)]TJ T* [(porary)-349(populations,)-349(we)-349(consider)-349(each)-349(separately.)-349(Shown)-349(are)-349(the)-349(estimated)]TJ 0 -1.286 TD [(posterior)-360(density)-360(of)]TJ /T1_9 1 Tf 9.638 0 Td (R)Tj /T1_8 1 Tf 5 0 0 5 385.9214 400.8835 Tm (0)Tj 7 0 0 7 391.2245 401.8835 Tm [(for)-360(Old)-360(World)-360(and)-360(New)-360(World)-360(populations,)-360(respec-)]TJ -11.007 -1.286 Td [(tively.)-245(The)-245(curved)-245(black)-245(line)-245(shows)-245(the)-245(prior)-245(distribution.)-245(The)-245(gray)-245(histogram)]TJ 0 -1.286 TD [(shows)-316(the)-316(case)-316(in)-316(which)-316(we)-316(assume)-316(that)-316(there)-316(is)-316(no)-316(uncertainty)-316(in)-316(any)-316(SEIR)]TJ T* [(model)-273(parameter)-273(except)]TJ /T1_9 1 Tf 11.713 0 Td (R)Tj /T1_8 1 Tf 5 0 0 5 400.4429 373.8835 Tm (0)Tj 7 0 0 7 405.138 374.8835 Tm [(\(\221\221\036xed\222\222\),)-273(whereas)-273(the)-274(black-outlined)-274(histogram)]TJ -12.995 -1.286 Td [(shows)-368(the)-368(case)-368(in)-368(which)-368(we)-368(instead)-368(assume)-368(that)-368(all)-368(model)-368(parameters)-368(are)]TJ T* [(uncertain,)-386(and)-386(we)-386(have)-386(integrated)-386(out)-386(all)-386(of)-386(the)-386(other)-386(parameters)-386(\(\221\221vari-)]TJ T* [(able\222\222\).)-361(The)-361(gray)-361(histogram)-361(thus)-361(is)-361(equivalent)-361(to)-361(assuming)-361(that)-361(disease)-361(pa-)]TJ T* [(rameters)-252(besides)]TJ /T1_9 1 Tf 8.007 0 Td (R)Tj /T1_8 1 Tf 5 0 0 5 374.5035 337.8835 Tm (0)Tj 7 0 0 7 379.0481 338.8835 Tm [(have)-252(zero)-252(uncertainty,)-252(showing)-252(that)-252(such)-252(an)-252(assumption)]TJ -9.267 -1.286 Td [(conceals)-278(substantial)-278(uncertainty.)-278(Note)-278(differences)-278(in)-278(scales)-278(on)-278(the)-278(axes.)]TJ 6.5 0 0 6.5 51.6761 39.8835 Tm (Elderd)Tj /T1_9 1 Tf 3.306 0 Td [(et)-305(al.)]TJ /T1_8 1 Tf 46.611 0 Td (PNAS)Tj /T1_10 1 Tf 9.75 0 0 6.5 398.387 39.8835 Tm (\001)Tj /T1_7 1 Tf 6.5 0 0 6.5 406.5516 39.8835 Tm [(October)-305(17,)-305(2006)]TJ /T1_10 1 Tf 9.75 0 0 6.5 464.5673 39.8835 Tm (\001)Tj /T1_8 1 Tf 6.5 0 0 6.5 472.7319 39.8835 Tm [(vol.)-305(103)]TJ /T1_10 1 Tf 9.75 0 0 6.5 502.3931 39.8835 Tm (\001)Tj /T1_8 1 Tf 6.5 0 0 6.5 510.5577 39.8835 Tm [(no.)-305(42)]TJ /T1_10 1 Tf 9.75 0 0 6.5 535.5193 39.8835 Tm (\001)Tj /T1_7 1 Tf 6.5 0 0 6.5 543.6839 39.8835 Tm (15695)Tj /T1_11 1 Tf 0 6.5 -6.5 0 585.1761 79.8523 Tm (POPULATION)Tj 0.861 -1.231 Td (BIOLOGY)Tj ET q /GS2 gs 19 0 0 815.5 9 9 cm /Im0 Do Q endstream endobj 54 0 obj <> /Properties <> /XObject <> /Font <> /ProcSet [/PDF /Text /ImageC] >> /QInserted true /Contents 77 0 R /Parent 1 0 R /ArtBox [9 9 603 792] /BleedBox [9 9 603 792] /Type /Page >> endobj 80 0 obj <> endobj 81 0 obj <> endobj 83 0 obj <> stream HےHSS(쪎DrF8 H Xw3=1&A׷r\~+l7Q:oN"uj`,?WnbwM}ڽti=$_ש2߷d4&ϓ8j&34_}ro* ۗwzI7^a/Զs>U!|4(>)EԳ:Nnv'Bg?0RM,( CM{/ʷO0"}9l}> ~9"t~D?+u76I.uS9%u2;J֣j icDc }/שrC5y9Uj7o܁bƈ7?Ik·.|l}҅~[~}RFo - ZI֘1ͬ[. )ND080y 1;s.p8A`c Q("h"B:r6` ؑ 7mΏ@ H8Pߓ҄R]0]n;l-Ѻ" ȄLh? 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[(change)-487(if)-487(we)-487(carefully)-487(quantif)-30(y)-487(the)-487(uncert)-30(aint)-30(y)-487(in)-487(a)-487(model\222s)]TJ 0 -1.148 TD [(parameter)-338(value)20(s.)]TJ 1 -1.148 Td [(A)-202(final)-202(import)-30(ant)-202(point)-202(is)-202(that)-202(our)-202(method)-202(is)-202(not)-202(specific)-202(to)-202(the)]TJ -1 -1.148 Td [(SEIR)-185(model.)-185(Indeed,)-185(a)-185(Baye)20(sian)-185(approach)-185(even)-185(allows)-185(for)-185(ef)-30(fects)]TJ T* [(for)-309(which)-309(little)-309(quantit)-30(ative)-309(infor)-30(mation)-309(is)-309(available.)-309(For)-309(exam-)]TJ 0 -1.146 TD [(ple,)-331(in)-331(the)-331(absence)-331(of)-331(any)-331(relevant)-331(dat)-30(a,)-331(we)-331(have)-331(assumed)-331(that)]TJ T* [(dif)-30(ference)20(s)-411(bet)-30(ween)-411(historical)-411(and)-411(bioterrorism)-411(outbreaks)-411(are)]TJ T* [(negligible,)-313(but)-313(the)-313(Baye)20(sian)-313(f)-30(ramework)-313(c)-30(ould)-313(be)-313(used)-313(to)-313(inc)-30(or-)]TJ T* [(porate)-291(such)-291(dif)-30(ference)20(s)-291(in)-291(the)-291(for)-30(m)-291(of)-291(ex)-30(pert)-291(opin)-30(ion.)-291(Inc)-30(orpo-)]TJ T* [(rating)-605(ex)-30(pert)-605(opin)-30(ion,)-605(however,)-605(would)-605(increase)-605(g)-20(reatly)-605(the)]TJ 0 -1.147 TD [(overall)-316(uncert)-30(aint)-30(y;)-316(given)-316(that)-316(we)-316(have)-316(argued)-316(that)-316(uncert)-30(aint)-30(y)]TJ 0 -1.146 TD [(is)-296(likely)-296(to)-296(be)-296(high,)-296(it)-296(is)-296(c)-30(onser)-60(vative)-296(to)-296(assume)-296(that)-296(dif)-30(ference)20(s)]TJ T* [(f)-30(rom)-382(historical)-382(epidemics)-382(are)-382(negligible.)-382(Our)-382(f)-30(ramework)-382(simi-)]TJ T* [(larly)-261(allows)-261(for)-261(straightfor)-30(ward)-261(updating)-261(of)-261(parameter)-261(e)20(stimate)20(s)]TJ T* [(w)-40(ith)-487(new)-487(dat)-30(a)-487(in)-487(the)-487(event)-487(of)-487(an)-487(actual)-487(epidemic.)-487(Baye)20(sian)]TJ T* [(approache)20(s)-238(to)-238(e)20(stimating)-238(uncert)-30(aint)-30(y)-238(thus)-238(may)-238(be)-238(of)-238(w)-40(ide)20(spread)]TJ T* [(usefulne)20(ss)-338(in)-338(plann)-30(ing)-338(for)-338(epidemics.)]TJ /T1_1 1 Tf -0.0196 Tc 0 -2.035 TD (Methods)Tj 0 Tc 8 0 0 8 51.6761 126.7926 Tm [(Prior)-536(Construction.)]TJ /T1_0 1 Tf 0.005 Tc 9 0 0 9 125.457 126.7926 Tm [(Vague)-476(priors)-476(of)-30(ten)-476(are)-476(used)-476(when)-476(little)-476(is)]TJ -8.198 -1.147 Td [(k)-30(nown)-186(regarding)-186(parameter)-186(value)20(s.)-186(In)-186(our)-186(case,)-186(however,)-186(enough)]TJ 0 -1.147 TD [(is)-225(k)-30(nown)-225(regarding)-225(the)-225(prog)-20(re)20(ssion)-225(of)-225(smallpox)-225(that)-225(it)-225(is)-225(possible)]TJ T* [(to)-215(instead)-215(c)-30(onstr)-30(uct)-215(infor)-30(mative)-215(priors)-215(for)-215(most)-215(parameters.)-215(The)]TJ T* [(one)-228(exception)-228(is)-228(that)-228(by)-228(defin)-30(ition,)-228(we)-228(have)-228(no)-228(prior)-228(infor)-30(mation)]TJ 0 -1.146 TD (on)Tj /T1_2 1 Tf 0 Tc 9 0 1.3977 9 64.2883 75.2017 Tm (\006)Tj /T1_0 1 Tf 0.005 Tc 9 0 0 9 69.8326 75.2017 Tm [(,)-298(because)-298(it)-298(de)20(scribe)20(s)-298(the)-298(error)-298(bet)-30(ween)-298(the)-298(model)-298(and)-298(the)]TJ -2.017 -1.147 Td [(dat)-30(a,)-447(and)-447(so)-447(for)]TJ /T1_2 1 Tf 0 Tc 9 0 1.3977 9 121.5343 64.8835 Tm (\006)Tj /T1_0 1 Tf 0.005 Tc 9 0 0 9 127.0786 64.8835 Tm [(,)-447(we)-447(used)-447(a)-447(vague)-447(prior.)-447(A)-30(lso,)-447(we)-447(did)-447(not)]TJ 20.789 74.444 Td [(ex)-30(plicitly)-422(model)-422(the)-422(c)-30(orrelations)-422(bet)-30(ween)-422(disease)-422(parameters.)]TJ 0 -1.136 TD [(Because)-354(we)-354(have)-354(no)-354(prior)-354(infor)-30(mation)-354(regarding)-354(such)-354(c)-30(orrela-)]TJ T* [(tions,)-353(including)-353(them)-353(would)-353(have)-353(required)-353(vague)-353(priors,)-353(which)]TJ T* [(probably)-338(would)-338(have)-338(re)20(sulted)-338(in)-338(even)-338(higher)-338(uncert)-30(aint)-30(y.)]TJ 1 -1.136 Td [(For)-473(the)-473(remain)-30(ing)-473(parameters,)-473(we)-473(first)-473(chose)-473(distributions)]TJ -1 -1.136 Td [(based)-499(on)-499(st)-30(andard)-499(st)-30(atistical)-499(c)-30(onsiderations.)-499(For)-499(the)-499(disease)]TJ T* [(reproductive)-235(rate)]TJ /T1_3 1 Tf 0 Tc 7.681 0 Td (R)Tj /T1_0 1 Tf 6.5 0 0 6 389.3936 672.2699 Tm (0)Tj 0.005 Tc 9 0 0 9 392.675 673.5199 Tm [(,)-235(we)-235(used)-235(a)-235(log-nor)-30(mal)-235(distribution,)-235(to)-235(allow)]TJ -8.722 -1.136 Td [(for)-331(a)-331(long)-331(t)-30(ail,)-331(as)-331(in)-331(Fig.)-331(1.)-331(For)-331(the)-331(infectious)-331(period)-331(1)]TJ /T1_4 1 Tf 0 Tc 23.922 0 Td (\002)Tj /T1_2 1 Tf 9 0 1.3977 9 534.0212 663.2926 Tm (\002)Tj /T1_0 1 Tf 0.005 Tc 9 0 0 9 542.0477 663.2926 Tm [(,)-331(and)]TJ -25.319 -1.136 Td [(for)-265(the)-265(rate)-265(of)-265(mov)-40(ing)-264(f)-30(rom)-264(latenc)-30(y)-265(to)-265(infectiousne)20(ss)]TJ /T1_2 1 Tf 0 Tc 9 0 1.3977 9 520.636 653.0654 Tm (\004)Tj /T1_0 1 Tf 0.005 Tc 9 0 0 9 526.1803 653.0654 Tm [(,)-265(we)-265(used)]TJ -23.556 -1.136 Td [(gamma)-251(distributions,)-251(which)-251(gave)-251(a)-251(good)-251(fit)-251(to)-251(dat)-30(a)-251(\(19)-90(\22622\).)-251(The)]TJ 0 -1.136 TD [(latent)-324(period)-324(usually)-324(is)-324(split)-324(into)-324(a)-324(period)-324(bet)-30(ween)-324(c)-30(ont)-30(act)-324(and)]TJ T* [(in)-30(itial)-349(fever,)-349(and)-349(a)-349(period)-349(bet)-30(ween)-349(fever)-349(and)-349(rash)-349([c)-30(ontrar)-60(y)-349(to)]TJ T* [(prev)-40(ious)-208(models)-208(\(5,)-208(11\),)-208(there)-208(is)-208(little)-208(ev)-40(idence)-208(for)-208(infectiousne)20(ss)]TJ T* [(during)-335(the)-335(latter)-335(period)-335(\(14,)-335(22\)].)-335(We)-335(therefore)-335(included)-335(sepa-)]TJ T* [(rate)-296(priors)-296(for)-296(each)-296(transition,)-296(sy)-30(mbolized)-296(as)]TJ /T1_2 1 Tf 0 Tc 9 0 1.3977 9 491.6391 591.7017 Tm (\004)Tj /T1_0 1 Tf 6.5 0 0 6 497.1833 590.4517 Tm (1)Tj 0.005 Tc 9 0 0 9 503.1323 591.7017 Tm (and)Tj /T1_2 1 Tf 0 Tc 9 0 1.3977 9 520.2277 591.7017 Tm (\004)Tj /T1_0 1 Tf 6.5 0 0 6 525.7719 590.4517 Tm (2)Tj 0.005 Tc 9 0 0 9 529.0533 591.7017 Tm [(,)-296(re)20(spec-)]TJ -23.875 -1.136 Td [(tively.)-221(Finally,)-221(for)-221(the)-221(f)-30(raction)-221(dying)]TJ /T1_2 1 Tf 0 Tc 9 0 1.3977 9 453.4952 581.4745 Tm (\005)Tj /T1_0 1 Tf 0.005 Tc 9 0 0 9 459.5434 581.4745 Tm [(,)-221(which)-221(by)-221(defin)-30(ition)-221(is)]TJ /T1_2 1 Tf 0 Tc 9.761 0 Td (\b)Tj /T1_0 1 Tf 0.005 Tc 0.838 0 Td (1,)Tj -26.751 -1.136 Td [(we)-267(used)-267(a)-267(bet)-30(a)-267(distribution,)-267(c)-30(ommonly)-267(used)-267(to)-267(model)-267(f)-30(ractional)]TJ T* [(quantitie)20(s.)-536(Because)]TJ /T1_2 1 Tf 0 Tc 9 0 1.3977 9 396.3848 561.0199 Tm (\005)Tj /T1_0 1 Tf 0.005 Tc 9 0 0 9 407.2597 561.0199 Tm [(is)-536(particularly)-536(uncert)-30(ain,)-536(we)-536(placed)-536(a)]TJ -10.343 -1.136 Td [(hyperprior)-214(on)-214(the)-214(parameters)-214(of)]TJ /T1_2 1 Tf 0 Tc 9 0 1.3977 9 439.3436 550.7926 Tm (\005)Tj /T1_0 1 Tf 0.005 Tc 9 0 0 9 445.3918 550.7926 Tm [(\222s)-214(prior,)-214(such)-214(that)-214(its)-214(mean)-214(was)]TJ -14.58 -1.135 Td [(drawn)-223(f)-30(rom)-223(a)-223(bet)-30(a)-223(distribution,)-223(whereas)-223(the)-223(scale)-223(parameter)-223(was)]TJ 0 -1.135 TD [(drawn)-284(f)-30(rom)-284(a)-284(gamma)-284(distribution.)-284(As)-284(a)-284(re)20(sult,)-284(the)-284(prior)-284(densit)-30(y)]TJ T* (for)Tj /T1_2 1 Tf 0 Tc 9 0 1.3977 9 328.1587 520.1449 Tm (\005)Tj /T1_0 1 Tf 0.005 Tc 9 0 0 9 336.7495 520.1449 Tm [(is)-282(ef)-30(fectively)-282(a)-282(mixture)-282(of)-283(bet)-30(a)-282(densitie)20(s,)-283(and,)-282(therefore,)-283(it)]TJ -2.508 -1.135 Td [(has)-338(longer)-338(t)-30(ails)-338(than)-338(a)-338(simple)-338(bet)-30(a)-338(den)-30(isit)-30(y.)]TJ 0.0199 Tc 1 -1.135 Td [(The)-288(parameters)-288(of)-288(the)-288(priors)-288(were)-288(t)-30(aken)-288(f)-30(rom)-288(the)-288(smallpox)]TJ -1 -1.135 Td [(literature.)-371(For)]TJ /T1_3 1 Tf 0 Tc 6.812 0 Td (R)Tj /T1_0 1 Tf 6.5 0 0 6 381.7016 488.2472 Tm (0)Tj 0.0199 Tc 9 0 0 9 385.0824 489.4972 Tm [(,)-371(we)-371(used)-371(a)-371(median)-371(of)-371(4,)-371(the)-371(midpoint)-371(of)-371(a)]TJ -7.878 -1.135 Td [(range)-653(based)-653(on)-653(immun)-30(ization)-653(rate)20(s)-653(before)-653(smallpox)-653(was)]TJ T* [(eliminated)-245(f)-30(rom)-245(general)-245(circulation)-245(\(2\).)-245(The)-245(credible)-245(inter)-60(vals)]TJ T* (for)Tj /T1_3 1 Tf 0 Tc 1.927 0 Td (R)Tj /T1_0 1 Tf 6.5 0 0 6 337.7343 457.5995 Tm (0)Tj 0.0199 Tc 9 0 0 9 346.6151 458.8495 Tm [(were)-611(chosen)-611(to)-611(enc)-30(ompass)-611(the)-611(range)-611(of)-611(prev)-40(ious)]TJ -3.604 -1.135 Td [(e)20(stimate)20(s)-276(\(3\).)-276(The)-276(priors)-276(on)-276(1)]TJ /T1_4 1 Tf 0 Tc 13.185 0 Td (\002)Tj /T1_2 1 Tf 9 0 1.3977 9 437.5153 448.6335 Tm (\002)Tj /T1_0 1 Tf 9 0 0 9 445.1867 448.6335 Tm (,)Tj /T1_2 1 Tf 9 0 1.3977 9 450.1042 448.6335 Tm (\004)Tj /T1_0 1 Tf 6.5 0 0 6 455.782 447.3835 Tm (1)Tj 0.0199 Tc 9 0 0 9 459.1628 448.6335 Tm [(,)-276(and)]TJ /T1_2 1 Tf 0 Tc 9 0 1.3977 9 481.3973 448.6335 Tm (\004)Tj /T1_0 1 Tf 6.5 0 0 6 487.075 447.3835 Tm (2)Tj 0.0199 Tc 9 0 0 9 492.9445 448.6335 Tm [(were)-276(c)-30(onstr)-30(ucted)]TJ -19.863 -1.135 Td [(by)-431(fitting)-431(gamma)-431(distributions)-431(directly)-431(to)-431(literature)-431(dat)-30(a)-431(on)]TJ T* [(smallpox-infected)-295(indiv)-40(iduals)-295(\(19)-90(\22622\).)-295(Because)-295(of)-295(dif)-30(ference)20(s)]TJ T* [(in)-222(the)-222(epidemiological)-222(histor)-60(y)-222(of)-222(smallpox)-222(bet)-30(ween)-222(c)-30(ontinents,)]TJ T* [(we)-547(ex)-30(pected)-547(dif)-30(ference)20(s)-547(in)-547(smallpox)-547(transmission)-547(bet)-30(ween)]TJ 0 -1.135 TD [(prev)-40(iously)-259(unex)-30(posed)-259(New)-259(World)-259(and)-259(prev)-40(iously)-259(ex)-30(posed)-259(Old)]TJ T* [(World)-357(\(or)-357(Old)-357(World)-357(de)20(scent\))-357(populations.)-357(We)-357(therefore)-357(fit)]TJ T* [(the)-327(model)-327(to)-327(epidemics)-327(f)-30(rom)-327(the)-327(t)-30(wo)-327(hemisphere)20(s)-327(separately)]TJ T* [(\(Fig.)-412(2\),)-412(and)-412(we)-412(assumed)-412(distinct)-412(value)20(s)-412(of)]TJ /T1_2 1 Tf 0 Tc 9 0 1.3977 9 495.9929 366.9062 Tm (\005)Tj /T1_0 1 Tf 0.0199 Tc 9 0 0 9 505.8877 366.9062 Tm [(for)-412(each.)-412(The)]TJ -21.301 -1.135 Td [(mean)-600(of)-600(the)-600(prior)-600(on)]TJ /T1_2 1 Tf 0 Tc 9 0 1.3977 9 414.452 356.6904 Tm (\005)Tj /T1_0 1 Tf 0.0199 Tc 9 0 0 9 426.0371 356.6904 Tm [(for)-600(Old)-600(World)-600(populations)-600(was)]TJ -12.429 -1.135 Td [(e)20(stimated)-373(f)-30(rom)-373(k)-30(nown)-373(rate)20(s,)-373(centered)-373(around)-373(a)-373(rate)-373(of)-373(16%)]TJ 0 -1.135 TD [(and)-272(w)-40(ith)-272(a)-272(95%)-272(credible)-272(inter)-60(val)-272(of)-272(\(3%,)-272(35%\))-272(\(Table)-272(1\).)-272(The)]TJ T* [(mean)-382(fat)-30(alit)-30(y)-382(rate)-382(for)-382(the)-382(New)-382(World)-382(populations)-382(was)-382(49%,)]TJ T* [(based)-461(on)-461(mort)-30(alit)-30(y)-461(in)-461(an)-461(epidemic)-461(among)-461(prev)-40(iously)-461(unex-)]TJ 0 -1.135 TD [(posed)-300(male)-300(slave)20(s)-300(in)-300(Puerto)-300(Ric)-30(o)-300(\(23\).)-300(The)-300(prior)-300(variance)-300(for)]TJ T* [(the)-299(New)-299(World)-299(fat)-30(alit)-30(y)-299(rate)-299(then)-299(was)-299(adjusted)-299(so)-299(that)-299(95%)-299(of)]TJ T* [(the)-353(distribution)-352(ranged)-353(f)-30(rom)-352(8%)-352(to)-353(90%.)]TJ 0.005 Tc 1 -1.135 Td [(Mathematically,)-338(the)-338(priors)-338(can)-338(be)-338(ex)-30(pre)20(ssed)-338(as)]TJ /T1_3 1 Tf 0 Tc 2.853 -2.046 Td (R)Tj /T1_0 1 Tf 0.02 Tc 6.3977 0 0 5.7614 355.0672 254.9602 Tm (0,)Tj /T1_3 1 Tf 0 Tc 0.79 0 Td (e)Tj /T1_4 1 Tf 9 0 0 9 364.9843 256.5511 Tm (\003)Tj /T1_5 1 Tf 0.0199 Tc 1.075 0 Td (LN)Tj /T1_6 1 Tf 0 Tc 1.41 0 Td (\003)Tj /T1_3 1 Tf 0.418 0 Td (m)Tj 6.3977 0 0 5.7614 399.2406 254.9602 Tm (e)Tj /T1_0 1 Tf 9 0 0 9 402.1891 256.5511 Tm (,)Tj /T1_2 1 Tf 9 0 1.3977 9 408.2174 256.5511 Tm (\006)Tj /T1_3 1 Tf 6.3977 0 0 5.7614 414.4803 254.6648 Tm (R)Tj /T1_0 1 Tf 0.0329 Tc 4.5 0 0 4.5 418.9834 253.1733 Tm (0,)Tj /T1_3 1 Tf 0 Tc 0.816 0 Td (e)Tj /T1_0 1 Tf 6.3977 0 0 5.7614 414.487 260.4261 Tm (2)Tj /T1_6 1 Tf 9 0 0 9 424.7285 256.5511 Tm (\004)Tj /T1_0 1 Tf 0.418 0 Td (,)Tj /T1_3 1 Tf 1.42 0 Td (R)Tj /T1_0 1 Tf 0.0329 Tc 6.3977 0 0 5.7614 448.0708 254.9602 Tm (0,)Tj /T1_3 1 Tf 0 Tc 0.816 0 Td (u)Tj /T1_4 1 Tf 9 0 0 9 458.9645 256.5511 Tm (\003)Tj /T1_5 1 Tf 0.005 Tc 1.14 0 Td (LN)Tj /T1_6 1 Tf 0 Tc 1.38 0 Td (\003)Tj /T1_3 1 Tf 0.418 0 Td (m)Tj 6.3977 0 0 5.7614 493.539 254.9602 Tm (u)Tj /T1_0 1 Tf 9 0 0 9 497.2167 256.5511 Tm (,)Tj /T1_2 1 Tf 9 0 1.3977 9 503.2451 256.5511 Tm (\006)Tj /T1_3 1 Tf 6.3977 0 0 5.7614 509.5081 254.6648 Tm (R)Tj /T1_0 1 Tf 0.0329 Tc 4.5 0 0 4.5 514.0111 253.1733 Tm (0,)Tj /T1_3 1 Tf 0 Tc 0.816 0 Td (u)Tj /T1_0 1 Tf 6.3977 0 0 5.7614 509.5136 260.4261 Tm (2)Tj /T1_6 1 Tf 9 0 0 9 520.2693 256.5511 Tm (\004)Tj /T1_0 1 Tf 0.418 0 Td (,)Tj /T1_3 1 Tf -18.462 -2.248 Td (p)Tj /T1_6 1 Tf 0.527 0 Td (\003)Tj /T1_2 1 Tf 9 0 1.3977 9 365.787 236.321 Tm (\006)Tj /T1_3 1 Tf 6.3977 0 0 5.7614 371.4647 234.4347 Tm (e)Tj /T1_0 1 Tf 0 1 Td (2)Tj /T1_6 1 Tf 0.2898 Tc 9 0 0 9 374.7939 236.321 Tm (\004\005)Tj /T1_0 1 Tf 0.0199 Tc 1.579 0 Td (1,)Tj /T1_2 1 Tf 0 Tc 9 0 1.3977 9 405.2961 236.321 Tm (\006)Tj /T1_3 1 Tf 6.3977 0 0 5.7614 410.9738 234.4347 Tm (e)Tj /T1_0 1 Tf 0 1 Td (2)Tj /T1_2 1 Tf 9 0 0 9 416.3001 236.321 Tm (\t)Tj /T1_0 1 Tf 0.0199 Tc 1.075 0 Td (0,)Tj /T1_3 1 Tf 0 Tc 1.81 0 Td (p)Tj /T1_6 1 Tf 0.527 0 Td (\003)Tj /T1_2 1 Tf 9 0 1.3977 9 450.1772 236.321 Tm (\006)Tj /T1_3 1 Tf 6.3977 0 0 5.7614 455.8549 234.4347 Tm (u)Tj /T1_0 1 Tf 0 1 Td (2)Tj /T1_6 1 Tf 0.2898 Tc 9 0 0 9 459.4503 236.321 Tm (\004\005)Tj /T1_0 1 Tf 0.0199 Tc 1.579 0 Td (1,)Tj /T1_2 1 Tf 0 Tc 9 0 1.3977 9 489.9525 236.321 Tm (\006)Tj /T1_3 1 Tf 6.3977 0 0 5.7614 495.6303 234.4347 Tm (u)Tj /T1_0 1 Tf 0 1 Td (2)Tj /T1_2 1 Tf 9 0 0 9 501.2228 236.321 Tm (\t)Tj /T1_0 1 Tf 0.0199 Tc 1.075 0 Td (0,)Tj /T1_2 1 Tf 0 Tc 9 0 1.3977 9 413.1989 210.5739 Tm (\004)Tj 9 0 0 9 420.8738 210.5739 Tm (\001)Tj /T1_0 1 Tf 2.463 0.812 Td (1)Tj ET 0 0 0 1 K 0.25 w 10 M 0 j 0 J []0 d 430.545 213.824 m 460.222 213.824 l S BT /T1_2 1 Tf 9 0 1.3977 9 430.5455 204.9005 Tm (\004)Tj /T1_0 1 Tf 6.3977 0 0 5.7614 436.2232 203.3096 Tm (1)Tj /T1_2 1 Tf 9 0 0 9 441.5471 204.9005 Tm (\n)Tj 9 0 1.3977 9 451.2199 204.9005 Tm (\004)Tj /T1_0 1 Tf 6.3977 0 0 5.7614 456.8976 203.3096 Tm (2)Tj 9 0 0 9 460.2243 210.5738 Tm (,)Tj /T1_2 1 Tf 9 0 1.3977 9 373.6847 186.7528 Tm (\004)Tj /T1_0 1 Tf 6.3977 0 0 5.7614 379.3624 185.1619 Tm (1)Tj /T1_4 1 Tf 9 0 0 9 384.6863 186.7528 Tm (\003)Tj /T1_7 1 Tf 1.075 0 Td (\001)Tj /T1_6 1 Tf 0.687 0 Td (\003)Tj /T1_0 1 Tf 0.005 Tc 0.418 0 Td (mean)Tj /T1_2 1 Tf 0 Tc 2.598 0 Td (\001)Tj /T1_0 1 Tf 0.0849 Tc 1.14 0 Td [(2.6,)-335(v)80(a)80(r)]TJ /T1_2 1 Tf 0 Tc 3.741 0 Td (\001)Tj /T1_0 1 Tf 0.0849 Tc 1.14 0 Td (0.6)Tj /T1_6 1 Tf 0 Tc 1.505 0 Td (\004)Tj /T1_0 1 Tf 0.418 0 Td (,)Tj /T1_2 1 Tf 9 0 1.3977 9 368.6222 168.6051 Tm (\004)Tj /T1_0 1 Tf 6.3977 0 0 5.7614 374.2999 167.0142 Tm (2)Tj /T1_4 1 Tf 9 0 0 9 382.0527 168.6051 Tm (\003)Tj /T1_7 1 Tf 1.345 0 Td (\001)Tj /T1_6 1 Tf 0.687 0 Td (\003)Tj /T1_0 1 Tf 0.005 Tc 0.418 0 Td (mean)Tj /T1_2 1 Tf 0 Tc 2.598 0 Td (\001)Tj /T1_0 1 Tf 0.0849 Tc 1.14 0 Td [(12.3,)-335(v)80(a)80(r)]TJ /T1_2 1 Tf 0 Tc 4.325 0 Td (\001)Tj /T1_0 1 Tf 0.0849 Tc 1.14 0 Td (6.1)Tj /T1_6 1 Tf 0 Tc 1.505 0 Td (\004)Tj /T1_0 1 Tf 0.418 0 Td (,)Tj -15.344 -2.016 Td (1)Tj /T1_4 1 Tf 0.52 0 Td (\002)Tj /T1_2 1 Tf 9 0 1.3977 9 375.4911 150.4574 Tm (\002)Tj /T1_4 1 Tf 9 0 0 9 385.1 150.4574 Tm (\003)Tj /T1_6 1 Tf 0.0199 Tc 1.345 0 Td (\006\003)Tj /T1_0 1 Tf 0.984 0 Td (mean)Tj /T1_2 1 Tf 0 Tc 2.657 0 Td (\001)Tj /T1_0 1 Tf 0.0849 Tc 1.14 0 Td [(16.0,)-335(v)80(a)80(r)]TJ /T1_2 1 Tf 0 Tc 4.325 0 Td (\001)Tj /T1_0 1 Tf 0.0849 Tc 1.14 0 Td (8.0)Tj /T1_6 1 Tf 0 Tc 1.505 0 Td (\004)Tj /T1_0 1 Tf 0.418 0 Td (,)Tj /T1_2 1 Tf 9 0 1.3977 9 361.8551 132.3097 Tm (\005)Tj /T1_3 1 Tf 6.3977 0 0 5.7614 368.0369 130.7188 Tm (e)Tj /T1_4 1 Tf 9 0 0 9 375.329 132.3097 Tm (\003)Tj /T1_5 1 Tf 0.0199 Tc 1.345 0 Td (Be)Tj /T1_6 1 Tf 0 Tc 1.147 0 Td (\003)Tj /T1_3 1 Tf 0.418 0 Td (a)Tj 6.3977 0 0 5.7614 406.8575 130.7188 Tm (e)Tj /T1_0 1 Tf 9 0 0 9 409.806 132.3097 Tm (,)Tj /T1_3 1 Tf 0.67 0 Td (b)Tj 6.3977 0 0 5.7614 421.1613 130.7188 Tm (e)Tj /T1_6 1 Tf 9 0 0 9 424.1097 132.3097 Tm (\004)Tj /T1_0 1 Tf 0.418 0 Td (,)Tj /T1_2 1 Tf 9 0 1.3977 9 440.6491 132.3097 Tm (\005)Tj /T1_3 1 Tf 6.3977 0 0 5.7614 447.4161 130.7188 Tm (u)Tj /T1_4 1 Tf 9 0 0 9 456.1052 132.3097 Tm (\003)Tj /T1_5 1 Tf 0.005 Tc 1.475 0 Td (Be)Tj /T1_6 1 Tf 0 Tc 1.117 0 Td (\003)Tj /T1_3 1 Tf 0.418 0 Td (a)Tj 6.3977 0 0 5.7614 488.5371 130.7188 Tm (u)Tj /T1_0 1 Tf 9 0 0 9 492.2149 132.3097 Tm (,)Tj /T1_3 1 Tf 0.67 0 Td (b)Tj 6.3977 0 0 5.7614 503.5703 130.7188 Tm (u)Tj /T1_6 1 Tf 9 0 0 9 507.248 132.3097 Tm (\004)Tj /T1_0 1 Tf 0.418 0 Td (,)Tj /T1_5 1 Tf 0.0199 Tc 4.211 0.667 Td ([3])Tj /T1_3 1 Tf 0 Tc -21.808 -2.683 Td (a)Tj 6.3977 0 0 5.7614 357.4019 112.571 Tm (e)Tj ET 343.006 110.108 m 369.903 110.108 l S BT /T1_3 1 Tf 9 0 0 9 343.0057 101.1847 Tm (a)Tj 6.3977 0 0 5.7614 347.7655 99.5938 Tm (e)Tj /T1_2 1 Tf 9 0 0 9 352.6287 101.1847 Tm (\n)Tj /T1_3 1 Tf 1.075 0 Td (b)Tj 6.3977 0 0 5.7614 367.0433 99.5938 Tm (e)Tj /T1_4 1 Tf 9 0 0 9 374.3355 106.858 Tm (\003)Tj /T1_5 1 Tf 0.0199 Tc 1.345 0 Td (Be)Tj /T1_6 1 Tf 0 Tc 1.147 0 Td (\003)Tj /T1_0 1 Tf 0.0849 Tc 0.418 0 Td [(5,)-335(17)]TJ /T1_6 1 Tf 0 Tc 2.425 0 Td (\004)Tj /T1_0 1 Tf 0.418 0 Td (,)Tj /T1_3 1 Tf 2.601 0.812 Td (a)Tj 6.3977 0 0 5.7614 454.8516 112.5711 Tm (u)Tj ET 438.866 110.108 m 469.145 110.108 l S BT /T1_3 1 Tf 9 0 0 9 438.8665 101.1847 Tm (a)Tj 6.3977 0 0 5.7614 444.2115 99.5938 Tm (u)Tj /T1_2 1 Tf 9 0 0 9 449.8865 101.1847 Tm (\n)Tj /T1_3 1 Tf 1.14 0 Td (b)Tj 6.3977 0 0 5.7614 465.4716 99.5938 Tm (u)Tj /T1_4 1 Tf 9 0 0 9 474.1607 106.858 Tm (\003)Tj /T1_5 1 Tf 0.005 Tc 1.475 0 Td (Be)Tj /T1_6 1 Tf 0 Tc 1.117 0 Td (\003)Tj /T1_0 1 Tf 0.0849 Tc 0.418 0 Td [(4,)-335(4.5)]TJ /T1_6 1 Tf 0 Tc 2.759 0 Td (\004)Tj /T1_0 1 Tf 0.418 0 Td (,)Tj /T1_3 1 Tf -17.502 -2.647 Td (a)Tj 6.3977 0 0 5.7614 377.0865 81.446 Tm (e)Tj /T1_4 1 Tf 9 0 0 9 384.3787 83.0369 Tm (\003)Tj /T1_7 1 Tf 1.345 0 Td (\001)Tj /T1_6 1 Tf 0.687 0 Td (\003)Tj /T1_0 1 Tf 0.005 Tc 0.418 0 Td (mean)Tj /T1_2 1 Tf 0 Tc 2.598 0 Td (\001)Tj /T1_0 1 Tf 0.0849 Tc 1.14 0 Td [(30,)-335(v)80(a)80(r)]TJ /T1_2 1 Tf 0 Tc 3.406 0 Td (\001)Tj /T1_0 1 Tf 0.0849 Tc 1.14 0 Td (150)Tj /T1_6 1 Tf 0 Tc 1.755 0 Td (\004)Tj /T1_0 1 Tf 0.418 0 Td (,)Tj /T1_3 1 Tf -13.408 -2.016 Td (a)Tj 6.3977 0 0 5.7614 384.6177 63.2983 Tm (u)Tj /T1_4 1 Tf 9 0 0 9 392.6393 64.8892 Tm (\003)Tj /T1_7 1 Tf 1.345 0 Td (\001)Tj /T1_6 1 Tf 0.687 0 Td (\003)Tj /T1_0 1 Tf 0.005 Tc 0.418 0 Td (mean)Tj /T1_2 1 Tf 0 Tc 2.598 0 Td (\001)Tj /T1_0 1 Tf 0.005 Tc 1.14 0 Td [(4)-80(,)-415(var)]TJ /T1_2 1 Tf 0 Tc 2.821 0 Td (\001)Tj /T1_0 1 Tf 1.14 0 Td (4)Tj /T1_6 1 Tf 0.585 0 Td (\004)Tj /T1_0 1 Tf 0.418 0 Td (,)Tj ET /Document /MC0 BDC q 51.676 450.884 247.889 289.295 re W n 0 0 0 0.202 K 0.341 w 1 j 1 J /GS1 gs 121.965 629.659 m 121.965 629.659 l 121.779 629.659 m 121.779 629.659 l 121.592 629.659 m 121.592 629.659 l 121.41 629.659 m 121.41 629.659 l 121.224 629.659 m 121.224 629.659 l 121.037 629.659 m 121.037 629.659 l 120.85 629.659 m 120.85 629.659 l 120.668 629.659 m 120.668 629.659 l 120.482 629.659 m 120.482 629.659 l 120.295 629.659 m 120.295 629.659 l 120.113 629.659 m 120.113 629.659 l 119.927 629.659 m 119.927 629.659 l 119.74 629.659 m 119.74 629.659 l 119.554 629.659 m 119.554 629.659 l 119.371 629.659 m 119.371 629.659 l 119.185 629.659 m 119.185 629.659 l 118.998 629.659 m 118.998 629.659 l 118.811 629.659 m 118.811 629.659 l 118.629 629.659 m 118.629 629.659 l 118.443 629.659 m 118.443 629.659 l 118.256 629.659 m 118.256 629.659 l 118.074 629.659 m 118.074 629.659 l 117.888 629.659 m 117.888 629.659 l 117.701 629.659 m 117.701 629.659 l 117.515 629.659 m 117.515 629.659 l 117.332 629.659 m 117.332 629.659 l 117.146 629.659 m 117.146 629.659 l 116.959 629.659 m 116.959 629.659 l 116.773 629.659 m 116.773 629.659 l 116.591 629.659 m 116.591 629.659 l 116.404 629.659 m 116.404 629.659 l 116.218 629.659 m 116.218 629.659 l 116.036 629.659 m 116.036 629.659 l 115.849 629.659 m 115.849 629.659 l 115.662 629.659 m 115.662 629.659 l 115.476 629.659 m 115.476 629.659 l 115.293 629.659 m 115.293 629.659 l 115.107 629.659 m 115.107 629.659 l 114.92 629.659 m 114.92 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630.875 m 201.785 633.483 l 199.177 631.061 m 201.598 633.483 l 199.177 631.248 m 201.416 633.483 l 199.177 631.43 m 201.229 633.483 l 199.177 631.616 m 201.043 633.483 l 199.177 631.802 m 200.856 633.483 l 199.177 631.99 m 200.675 633.483 l 199.177 632.172 m 200.488 633.483 l 199.177 632.358 m 200.302 633.483 l 199.177 632.545 m 200.115 633.483 l 199.177 632.732 m 199.932 633.483 l 199.177 632.914 m 199.746 633.483 l 199.177 633.1 m 199.559 633.483 l 199.177 633.286 m 199.378 633.483 l 199.177 633.473 m 199.191 633.483 l 199.072 629.659 m 199.177 629.764 l 198.89 629.659 m 199.177 629.951 l 198.704 629.659 m 199.177 630.133 l 198.517 629.659 m 199.177 630.32 l 198.331 629.659 m 199.177 630.505 l 198.149 629.659 m 199.177 630.693 l 197.963 629.659 m 199.177 630.875 l 197.775 629.659 m 199.177 631.061 l 197.589 629.659 m 199.177 631.248 l 197.407 629.659 m 199.177 631.43 l 197.22 629.659 m 199.177 631.616 l 197.034 629.659 m 199.177 631.802 l 196.851 629.659 m 199.177 631.99 l 196.665 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629.659 m 297.879 629.659 l S Q 0 g /GS1 gs BT /T1_8 1 Tf 6.8264 0 0 6.8264 82.9954 614.9146 Tm [(0)-10400(200)-9845(400)]TJ ET 0.341 w 1 j 1 J 84.893 720.265 m 80.797 720.265 l 84.893 674.96 m 80.797 674.96 l 84.893 629.659 m 80.797 629.659 l 84.893 629.659 m 84.893 720.265 l S BT /T1_8 1 Tf 0 6.8264 -6.8264 0 75.0638 627.7615 Tm [(0)-5524(100)-4969(200)]TJ ET q 51.676 450.884 247.889 289.295 re W n 84.893 629.659 m 84.893 735.333 l 84.893 629.659 m 297.879 629.659 l S Q BT /T1_8 1 Tf 11.9999 0 0 12 70.2 729.8704 Tm (A)Tj 0.0001 Tc -0.0001 Tw 6.8264 0 0 6.8264 173.3051 708.9374 Tm (Median Fixed = 206 thousand)Tj 0 Tc 0.0003 Tw -11.814 -2.263 Td (Median Variable =)Tj 0 Tw 1.014 -1.5 Td (113 thousand)Tj ET q 51.676 450.884 247.889 289.295 re W n 0 0 0 0.202 K 95.542 487.634 m 106.192 498.283 l 95.542 487.815 m 106.192 498.465 l 95.542 488.002 m 106.192 498.651 l 95.542 488.189 m 106.192 498.839 l 95.542 488.376 m 106.192 499.024 l 95.542 488.557 m 106.192 499.207 l 95.542 488.744 m 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85.635 480.134 m 88.275 482.773 l 85.449 480.134 m 88.093 482.773 l 85.262 480.134 m 87.906 482.773 l 85.08 480.134 m 87.719 482.773 l 84.893 480.134 m 87.533 482.773 l 84.893 480.32 m 87.351 482.773 l 84.893 480.503 m 87.164 482.773 l 84.893 480.688 m 86.977 482.773 l 84.893 480.875 m 86.796 482.773 l 84.893 481.062 m 86.609 482.773 l 84.893 481.244 m 86.422 482.773 l 84.893 481.43 m 86.236 482.773 l 84.893 481.617 m 86.054 482.773 l 84.893 481.803 m 85.867 482.773 l 84.893 481.986 m 85.681 482.773 l 84.893 482.173 m 85.494 482.773 l 84.893 482.359 m 85.312 482.773 l 84.893 482.541 m 85.125 482.773 l 84.893 482.727 m 84.939 482.773 l S 106.192 507.735 m 116.841 518.385 l 106.192 507.922 m 116.841 518.571 l 106.192 508.103 m 116.841 518.753 l 106.192 508.291 m 116.841 518.939 l 106.192 508.477 m 116.841 519.127 l 106.192 508.659 m 116.841 519.307 l 106.192 508.845 m 116.841 519.495 l 106.192 509.032 m 116.841 519.681 l 106.192 509.219 m 116.841 519.868 l 106.192 509.401 m 116.841 520.05 l 106.192 509.587 m 116.841 520.236 l 106.192 509.774 m 116.841 520.424 l 106.192 509.961 m 116.841 520.609 l 106.192 510.142 m 116.841 520.792 l 106.192 510.33 m 116.841 520.978 l 106.192 510.515 m 116.841 521.164 l 106.192 510.698 m 116.841 521.346 l 106.192 510.885 m 116.841 521.533 l 106.192 511.071 m 116.841 521.721 l 106.192 511.258 m 116.841 521.906 l 106.192 511.439 m 116.841 522.089 l 106.192 511.626 m 116.841 522.275 l 106.192 511.813 m 116.841 522.462 l 106.192 512 m 116.841 522.648 l 106.192 512.181 m 116.841 522.831 l 106.192 512.368 m 116.841 523.017 l 106.192 512.554 m 116.841 523.203 l 106.192 512.737 m 116.841 523.385 l 106.192 512.923 m 116.841 523.572 l 106.192 513.109 m 116.841 523.76 l 106.192 513.297 m 116.841 523.945 l 106.192 513.478 m 116.841 524.128 l 106.192 513.664 m 116.841 524.314 l 106.192 513.851 m 116.841 524.501 l 106.192 514.038 m 116.841 524.687 l 106.192 514.221 m 116.841 524.869 l 106.192 514.407 m 116.841 525.056 l 106.192 514.594 m 116.841 525.243 l 106.192 514.78 m 116.841 525.429 l 106.192 514.962 m 116.841 525.611 l 106.192 515.149 m 116.841 525.798 l 106.192 515.336 m 116.841 525.984 l 106.192 515.517 m 116.841 526.167 l 106.192 515.703 m 116.841 526.353 l 106.192 515.89 m 116.841 526.54 l 106.192 516.077 m 116.8 526.68 l 106.192 516.259 m 116.614 526.68 l 106.192 516.445 m 116.427 526.68 l 106.192 516.633 m 116.245 526.68 l 106.192 516.819 m 116.058 526.68 l 106.192 517.001 m 115.872 526.68 l 106.192 517.187 m 115.685 526.68 l 106.192 517.374 m 115.503 526.68 l 106.192 517.556 m 115.316 526.68 l 106.192 517.743 m 115.13 526.68 l 106.192 517.929 m 114.943 526.68 l 106.192 518.116 m 114.761 526.68 l 106.192 518.298 m 114.575 526.68 l 106.192 518.484 m 114.388 526.68 l 106.192 518.672 m 114.206 526.68 l 106.192 518.857 m 114.019 526.68 l 106.192 519.04 m 113.833 526.68 l 106.192 519.226 m 113.646 526.68 l 106.192 519.413 m 113.464 526.68 l 106.192 519.595 m 113.278 526.68 l 106.192 519.781 m 113.091 526.68 l 106.192 519.969 m 112.904 526.68 l 106.192 520.155 m 112.722 526.68 l 106.192 520.337 m 112.536 526.68 l 106.192 520.523 m 112.349 526.68 l 106.192 520.71 m 112.167 526.68 l 106.192 520.896 m 111.98 526.68 l 106.192 521.078 m 111.794 526.68 l 106.192 521.265 m 111.607 526.68 l 106.192 521.452 m 111.425 526.68 l 106.192 521.634 m 111.239 526.68 l 106.192 521.82 m 111.052 526.68 l 106.192 522.007 m 110.866 526.68 l 106.192 522.193 m 110.684 526.68 l 106.192 522.376 m 110.497 526.68 l 106.192 522.562 m 110.31 526.68 l 106.192 522.749 m 110.128 526.68 l 106.192 522.935 m 109.942 526.68 l 106.192 523.117 m 109.755 526.68 l 106.192 523.304 m 109.569 526.68 l 106.192 523.491 m 109.387 526.68 l 106.192 523.677 m 109.2 526.68 l 106.192 523.859 m 109.013 526.68 l 106.192 524.046 m 108.827 526.68 l 106.192 524.232 m 108.645 526.68 l 106.192 524.414 m 108.458 526.68 l 106.192 524.601 m 108.271 526.68 l 106.192 524.788 m 108.09 526.68 l 106.192 524.974 m 107.903 526.68 l 106.192 525.156 m 107.716 526.68 l 106.192 525.343 m 107.53 526.68 l 106.192 525.529 m 107.348 526.68 l 106.192 525.716 m 107.161 526.68 l 106.192 525.898 m 106.975 526.68 l 106.192 526.085 m 106.788 526.68 l 106.192 526.271 m 106.606 526.68 l 106.192 526.453 m 106.419 526.68 l 106.192 526.64 m 106.233 526.68 l 106.023 480.134 m 106.192 480.302 l 105.837 480.134 m 106.192 480.489 l 105.655 480.134 m 106.192 480.671 l 105.468 480.134 m 106.192 480.857 l 105.282 480.134 m 106.192 481.044 l 105.095 480.134 m 106.192 481.23 l 104.913 480.134 m 106.192 481.413 l 104.726 480.134 m 106.192 481.598 l 104.539 480.134 m 106.192 481.786 l 104.358 480.134 m 106.192 481.968 l 104.171 480.134 m 106.192 482.154 l 103.985 480.134 m 106.192 482.341 l 103.798 480.134 m 106.192 482.526 l 103.616 480.134 m 106.192 482.71 l 103.429 480.134 m 106.192 482.896 l 103.243 480.134 m 106.192 483.083 l 103.056 480.134 m 106.192 483.269 l 102.874 480.134 m 106.192 483.451 l 102.687 480.134 m 106.192 483.637 l 102.501 480.134 m 106.192 483.824 l 102.319 480.134 m 106.192 484.007 l 102.132 480.134 m 106.192 484.193 l 101.946 480.134 m 106.192 484.38 l 101.759 480.134 m 106.192 484.566 l 101.577 480.134 m 106.192 484.749 l 101.391 480.134 m 106.192 484.934 l 101.204 480.134 m 106.192 485.121 l 101.018 480.134 m 106.192 485.307 l 100.835 480.134 m 106.192 485.49 l 100.649 480.134 m 106.192 485.677 l 100.462 480.134 m 106.192 485.863 l 100.28 480.134 m 106.192 486.046 l 100.093 480.134 m 106.192 486.232 l 99.907 480.134 m 106.192 486.419 l 99.72 480.134 m 106.192 486.605 l 99.539 480.134 m 106.192 486.787 l 99.351 480.134 m 106.192 486.973 l 99.165 480.134 m 106.192 487.16 l 98.978 480.134 m 106.192 487.347 l 98.796 480.134 m 106.192 487.529 l 98.61 480.134 m 106.192 487.716 l 98.423 480.134 m 106.192 487.902 l 98.241 480.134 m 106.192 488.084 l 98.055 480.134 m 106.192 488.27 l 97.868 480.134 m 106.192 488.457 l 97.682 480.134 m 106.192 488.644 l 97.499 480.134 m 106.192 488.826 l 97.313 480.134 m 106.192 489.012 l 97.126 480.134 m 106.192 489.199 l 96.94 480.134 m 106.192 489.386 l 96.758 480.134 m 106.192 489.568 l 96.571 480.134 m 106.192 489.755 l 96.384 480.134 m 106.192 489.941 l 96.198 480.134 m 106.192 490.128 l 96.016 480.134 m 106.192 490.309 l 95.829 480.134 m 106.192 490.496 l 95.643 480.134 m 106.192 490.683 l 95.542 480.216 m 106.192 490.865 l 95.542 480.402 m 106.192 491.052 l 95.542 480.589 m 106.192 491.238 l 95.542 480.775 m 106.192 491.425 l 95.542 480.958 m 106.192 491.606 l 95.542 481.143 m 106.192 491.793 l 95.542 481.33 m 106.192 491.98 l 95.542 481.517 m 106.192 492.167 l 95.542 481.699 m 106.192 492.348 l 95.542 481.886 m 106.192 492.535 l 95.542 482.072 m 106.192 492.721 l 95.542 482.255 m 106.192 492.904 l 95.542 482.441 m 106.192 493.09 l 95.542 482.628 m 106.192 493.276 l 95.542 482.814 m 106.192 493.464 l 95.542 482.996 m 106.192 493.645 l 95.542 483.182 m 106.192 493.832 l 95.542 483.369 m 106.192 494.018 l 95.542 483.556 m 106.192 494.205 l 95.542 483.738 m 106.192 494.387 l 95.542 483.925 m 106.192 494.574 l 95.542 484.111 m 106.192 494.761 l 95.542 484.294 m 106.192 494.942 l 95.542 484.479 m 106.192 495.129 l 95.542 484.666 m 106.192 495.315 l 95.542 484.853 m 106.192 495.503 l 95.542 485.035 m 106.192 495.684 l 95.542 485.221 m 106.192 495.871 l 95.542 485.408 m 106.192 496.057 l 95.542 485.595 m 106.192 496.244 l 95.542 485.777 m 106.192 496.426 l 95.542 485.964 m 106.192 496.612 l 95.542 486.15 m 106.192 496.8 l 95.542 486.332 m 106.192 496.981 l 95.542 486.518 m 106.192 497.168 l 95.542 486.705 m 106.192 497.354 l 95.542 486.892 m 106.192 497.541 l 95.542 487.074 m 106.192 497.723 l 95.542 487.261 m 106.192 497.91 l 95.542 487.447 m 106.192 498.096 l S 115.662 480.134 m 116.841 481.312 l 115.476 480.134 m 116.841 481.499 l 115.293 480.134 m 116.841 481.681 l 115.107 480.134 m 116.841 481.868 l 114.92 480.134 m 116.841 482.053 l 114.734 480.134 m 116.841 482.241 l 114.552 480.134 m 116.841 482.422 l 114.365 480.134 m 116.841 482.609 l 114.179 480.134 m 116.841 482.796 l 113.997 480.134 m 116.841 482.978 l 113.81 480.134 m 116.841 483.165 l 113.623 480.134 m 116.841 483.351 l 113.437 480.134 m 116.841 483.538 l 113.255 480.134 m 116.841 483.72 l 113.068 480.134 m 116.841 483.906 l 112.882 480.134 m 116.841 484.093 l 112.695 480.134 m 116.841 484.279 l 112.513 480.134 m 116.841 484.462 l 112.327 480.134 m 116.841 484.648 l 112.14 480.134 m 116.841 484.835 l 111.953 480.134 m 116.841 485.021 l 111.771 480.134 m 116.841 485.203 l 111.584 480.134 m 116.841 485.389 l 111.398 480.134 m 116.841 485.576 l 111.216 480.134 m 116.841 485.759 l 111.03 480.134 m 116.841 485.945 l 110.843 480.134 m 116.841 486.132 l 110.656 480.134 m 116.841 486.318 l 110.474 480.134 m 116.841 486.501 l 110.288 480.134 m 116.841 486.687 l 110.101 480.134 m 116.841 486.874 l 109.914 480.134 m 116.841 487.06 l 109.732 480.134 m 116.841 487.242 l 109.546 480.134 m 116.841 487.429 l 109.359 480.134 m 116.841 487.615 l 109.177 480.134 m 116.841 487.798 l 108.991 480.134 m 116.841 487.984 l 108.804 480.134 m 116.841 488.171 l 108.618 480.134 m 116.841 488.357 l 108.435 480.134 m 116.841 488.539 l 108.248 480.134 m 116.841 488.725 l 108.062 480.134 m 116.841 488.912 l 107.875 480.134 m 116.841 489.099 l 107.694 480.134 m 116.841 489.281 l 107.507 480.134 m 116.841 489.468 l 107.32 480.134 m 116.841 489.654 l 107.138 480.134 m 116.841 489.837 l 106.952 480.134 m 116.841 490.023 l 106.765 480.134 m 116.841 490.21 l 106.579 480.134 m 116.841 490.396 l 106.396 480.134 m 116.841 490.578 l 106.21 480.134 m 116.841 490.764 l 106.192 480.302 m 116.841 490.951 l 106.192 480.489 m 116.841 491.138 l 106.192 480.671 m 116.841 491.32 l 106.192 480.857 m 116.841 491.507 l 106.192 481.044 m 116.841 491.693 l 106.192 481.23 m 116.841 491.88 l 106.192 481.413 m 116.841 492.061 l 106.192 481.598 m 116.841 492.248 l 106.192 481.786 m 116.841 492.435 l 106.192 481.968 m 116.841 492.617 l 106.192 482.154 m 116.841 492.803 l 106.192 482.341 m 116.841 492.99 l 106.192 482.526 m 116.841 493.177 l 106.192 482.71 m 116.841 493.359 l 106.192 482.896 m 116.841 493.545 l 106.192 483.083 m 116.841 493.732 l 106.192 483.269 m 116.841 493.919 l 106.192 483.451 m 116.841 494.1 l 106.192 483.637 m 116.841 494.287 l 106.192 483.824 m 116.841 494.473 l 106.192 484.007 m 116.841 494.656 l 106.192 484.193 m 116.841 494.843 l 106.192 484.38 m 116.841 495.029 l 106.192 484.566 m 116.841 495.216 l 106.192 484.749 m 116.841 495.397 l 106.192 484.934 m 116.841 495.584 l 106.192 485.121 m 116.841 495.77 l 106.192 485.307 m 116.841 495.958 l 106.192 485.49 m 116.841 496.139 l 106.192 485.677 m 116.841 496.326 l 106.192 485.863 m 116.841 496.512 l 106.192 486.046 m 116.841 496.695 l 106.192 486.232 m 116.841 496.881 l 106.192 486.419 m 116.841 497.067 l 106.192 486.605 m 116.841 497.255 l 106.192 486.787 m 116.841 497.436 l 106.192 486.973 m 116.841 497.623 l 106.192 487.16 m 116.841 497.809 l 106.192 487.347 m 116.841 497.996 l 106.192 487.529 m 116.841 498.179 l 106.192 487.716 m 116.841 498.365 l 106.192 487.902 m 116.841 498.552 l 106.192 488.084 m 116.841 498.733 l 106.192 488.27 m 116.841 498.92 l 106.192 488.457 m 116.841 499.106 l 106.192 488.644 m 116.841 499.294 l 106.192 488.826 m 116.841 499.475 l 106.192 489.012 m 116.841 499.662 l 106.192 489.199 m 116.841 499.848 l 106.192 489.386 m 116.841 500.035 l 106.192 489.568 m 116.841 500.217 l 106.192 489.755 m 116.841 500.403 l 106.192 489.941 m 116.841 500.591 l 106.192 490.128 m 116.841 500.777 l 106.192 490.309 m 116.841 500.959 l 106.192 490.496 m 116.841 501.145 l 106.192 490.683 m 116.841 501.332 l 106.192 490.865 m 116.841 501.514 l 106.192 491.052 m 116.841 501.701 l 106.192 491.238 m 116.841 501.887 l 106.192 491.425 m 116.841 502.074 l 106.192 491.606 m 116.841 502.256 l 106.192 491.793 m 116.841 502.442 l 106.192 491.98 m 116.841 502.629 l 106.192 492.167 m 116.841 502.815 l 106.192 492.348 m 116.841 502.998 l 106.192 492.535 m 116.841 503.184 l 106.192 492.721 m 116.841 503.371 l 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106.192 498.096 m 116.841 508.746 l 106.192 498.283 m 116.841 508.932 l 106.192 498.465 m 116.841 509.114 l 106.192 498.651 m 116.841 509.301 l 106.192 498.839 m 116.841 509.487 l 106.192 499.024 m 116.841 509.674 l 106.192 499.207 m 116.841 509.856 l 106.192 499.393 m 116.841 510.043 l 106.192 499.58 m 116.841 510.229 l 106.192 499.761 m 116.841 510.411 l 106.192 499.948 m 116.841 510.597 l 106.192 500.135 m 116.841 510.785 l 106.192 500.322 m 116.841 510.971 l 106.192 500.504 m 116.841 511.153 l 106.192 500.69 m 116.841 511.34 l 106.192 500.877 m 116.841 511.526 l 106.192 501.063 m 116.841 511.713 l 106.192 501.246 m 116.841 511.894 l 106.192 501.431 m 116.841 512.081 l 106.192 501.619 m 116.841 512.268 l 106.192 501.801 m 116.841 512.45 l 106.192 501.987 m 116.841 512.637 l 106.192 502.174 m 116.841 512.823 l 106.192 502.36 m 116.841 513.01 l 106.192 502.543 m 116.841 513.192 l 106.192 502.729 m 116.841 513.378 l 106.192 502.916 m 116.841 513.565 l 106.192 503.102 m 116.841 513.752 l 106.192 503.284 m 116.841 513.932 l 106.192 503.471 m 116.841 514.12 l 106.192 503.658 m 116.841 514.306 l 106.192 503.84 m 116.841 514.489 l 106.192 504.026 m 116.841 514.676 l 106.192 504.213 m 116.841 514.862 l 106.192 504.399 m 116.841 515.049 l 106.192 504.581 m 116.841 515.229 l 106.192 504.767 m 116.841 515.417 l 106.192 504.955 m 116.841 515.604 l 106.192 505.141 m 116.841 515.791 l 106.192 505.323 m 116.841 515.972 l 106.192 505.51 m 116.841 516.159 l 106.192 505.696 m 116.841 516.345 l 106.192 505.883 m 116.841 516.531 l 106.192 506.065 m 116.841 516.714 l 106.192 506.252 m 116.841 516.901 l 106.192 506.438 m 116.841 517.088 l 106.192 506.62 m 116.841 517.269 l 106.192 506.806 m 116.841 517.456 l 106.192 506.994 m 116.841 517.642 l 106.192 507.18 m 116.841 517.828 l 106.192 507.362 m 116.841 518.01 l 106.192 507.549 m 116.841 518.198 l S 116.841 504.854 m 127.49 515.504 l 116.841 505.036 m 127.49 515.685 l 116.841 505.222 m 127.49 515.872 l 116.841 505.41 m 127.49 516.059 l 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529.926 l 159.438 519.458 m 170.088 530.108 l 159.438 519.645 m 170.088 530.294 l 159.438 519.832 m 170.088 530.479 l S 170.088 508.053 m 180.737 518.703 l 170.088 508.236 m 180.737 518.885 l 170.088 508.423 m 180.737 519.072 l 170.088 508.609 m 180.737 519.258 l 170.088 508.796 m 180.737 519.445 l 170.088 508.977 m 180.737 519.627 l 170.088 509.164 m 180.737 519.812 l 170.088 509.35 m 180.737 520 l 170.088 509.533 m 180.737 520.181 l 170.088 509.72 m 180.737 520.369 l 170.088 509.906 m 180.737 520.555 l 170.088 510.093 m 180.737 520.742 l 170.088 510.275 m 180.737 520.924 l 170.088 510.462 m 180.737 521.109 l 170.088 510.647 m 180.737 521.297 l 170.088 510.834 m 180.737 521.483 l 170.088 511.016 m 180.737 521.666 l 170.088 511.203 m 180.737 521.852 l 170.088 511.389 m 180.737 522.039 l 170.088 511.571 m 180.737 522.221 l 170.088 511.759 m 180.737 522.408 l 170.088 511.945 m 180.737 522.594 l 170.088 512.132 m 180.737 522.78 l 170.088 512.313 m 180.737 522.963 l 170.088 512.5 m 180.737 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180.737 528.341 l 170.088 517.875 m 180.737 528.523 l 170.088 518.061 m 180.737 528.711 l 170.088 518.248 m 180.737 528.897 l 170.088 518.429 m 180.737 529.078 l 170.088 518.617 m 180.737 529.265 l 170.088 518.802 m 180.737 529.452 l 170.088 518.989 m 180.737 529.638 l 170.088 519.172 m 180.737 529.821 l 170.088 519.358 m 180.737 530.008 l 170.088 519.545 m 180.737 530.194 l 170.088 519.731 m 180.737 530.38 l 170.088 519.914 m 180.737 530.562 l 170.088 520.1 m 180.737 530.749 l 170.088 520.286 m 180.737 530.935 l 170.088 520.469 m 180.737 531.118 l 170.088 520.655 m 180.737 531.304 l 170.088 520.841 m 180.737 531.491 l 170.088 521.028 m 180.655 531.595 l 170.088 521.211 m 180.473 531.595 l 170.088 521.397 m 180.286 531.595 l 170.088 521.583 m 180.099 531.595 l 170.088 521.77 m 179.918 531.595 l 170.088 521.953 m 179.731 531.595 l 170.088 522.138 m 179.544 531.595 l 170.088 522.325 m 179.357 531.595 l 170.088 522.512 m 179.176 531.595 l 170.088 522.694 m 178.989 531.595 l 170.088 522.88 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173.614 531.595 l 170.088 528.255 m 173.428 531.595 l 170.088 528.442 m 173.241 531.595 l 170.088 528.629 m 173.059 531.595 l 170.088 528.81 m 172.873 531.595 l 170.088 528.997 m 172.686 531.595 l 170.088 529.182 m 172.5 531.595 l 170.088 529.371 m 172.318 531.595 l 170.088 529.552 m 172.131 531.595 l 170.088 529.739 m 171.944 531.595 l 170.088 529.926 m 171.758 531.595 l 170.088 530.108 m 171.576 531.595 l 170.088 530.294 m 171.389 531.595 l 170.088 530.479 m 171.202 531.595 l 170.088 530.668 m 171.02 531.595 l 170.088 530.849 m 170.834 531.595 l 170.088 531.036 m 170.647 531.595 l 170.088 531.222 m 170.461 531.595 l 170.088 531.409 m 170.279 531.595 l 170.088 531.592 m 170.092 531.595 l 169.974 480.134 m 170.088 480.247 l 169.787 480.134 m 170.088 480.434 l 169.6 480.134 m 170.088 480.621 l 169.419 480.134 m 170.088 480.803 l 169.232 480.134 m 170.088 480.989 l 169.045 480.134 m 170.088 481.176 l 168.859 480.134 m 170.088 481.362 l 168.676 480.134 m 170.088 481.545 l 168.49 480.134 m 170.088 481.731 l 168.303 480.134 m 170.088 481.918 l 168.117 480.134 m 170.088 482.104 l 167.935 480.134 m 170.088 482.286 l 167.748 480.134 m 170.088 482.473 l 167.562 480.134 m 170.088 482.659 l 167.38 480.134 m 170.088 482.842 l 167.193 480.134 m 170.088 483.028 l 167.007 480.134 m 170.088 483.215 l 166.82 480.134 m 170.088 483.401 l 166.638 480.134 m 170.088 483.583 l 166.451 480.134 m 170.088 483.77 l 166.264 480.134 m 170.088 483.957 l 166.078 480.134 m 170.088 484.143 l 165.896 480.134 m 170.088 484.325 l 165.71 480.134 m 170.088 484.511 l 165.523 480.134 m 170.088 484.698 l 165.341 480.134 m 170.088 484.88 l 165.154 480.134 m 170.088 485.066 l 164.968 480.134 m 170.088 485.254 l 164.781 480.134 m 170.088 485.44 l 164.599 480.134 m 170.088 485.622 l 164.412 480.134 m 170.088 485.808 l 164.226 480.134 m 170.088 485.995 l 164.039 480.134 m 170.088 486.181 l 163.857 480.134 m 170.088 486.364 l 163.671 480.134 m 170.088 486.551 l 163.484 480.134 m 170.088 486.737 l 163.302 480.134 m 170.088 486.919 l 163.115 480.134 m 170.088 487.105 l 162.928 480.134 m 170.088 487.293 l 162.742 480.134 m 170.088 487.479 l 162.56 480.134 m 170.088 487.661 l 162.374 480.134 m 170.088 487.847 l 162.187 480.134 m 170.088 488.034 l 162.001 480.134 m 170.088 488.221 l 161.818 480.134 m 170.088 488.402 l 161.632 480.134 m 170.088 488.59 l 161.445 480.134 m 170.088 488.776 l 161.259 480.134 m 170.088 488.963 l 161.076 480.134 m 170.088 489.144 l 160.89 480.134 m 170.088 489.331 l 160.703 480.134 m 170.088 489.517 l 160.521 480.134 m 170.088 489.7 l 160.335 480.134 m 170.088 489.887 l 160.148 480.134 m 170.088 490.073 l 159.962 480.134 m 170.088 490.26 l 159.78 480.134 m 170.088 490.441 l 159.593 480.134 m 170.088 490.629 l 159.438 480.166 m 170.088 490.814 l 159.438 480.352 m 170.088 491.001 l 159.438 480.534 m 170.088 491.183 l 159.438 480.721 m 170.088 491.37 l 159.438 480.907 m 170.088 491.556 l 159.438 481.09 m 170.088 491.738 l 159.438 481.276 m 170.088 491.926 l 159.438 481.463 m 170.088 492.112 l 159.438 481.649 m 170.088 492.299 l 159.438 481.831 m 170.088 492.48 l 159.438 482.018 m 170.088 492.667 l 159.438 482.203 m 170.088 492.853 l 159.438 482.39 m 170.088 493.04 l 159.438 482.573 m 170.088 493.222 l 159.438 482.76 m 170.088 493.409 l S 179.239 480.134 m 180.737 481.631 l 179.057 480.134 m 180.737 481.813 l 178.871 480.134 m 180.737 482 l 178.684 480.134 m 180.737 482.186 l 178.498 480.134 m 180.737 482.373 l 178.316 480.134 m 180.737 482.554 l 178.129 480.134 m 180.737 482.741 l 177.942 480.134 m 180.737 482.929 l 177.756 480.134 m 180.737 483.114 l 177.574 480.134 m 180.737 483.297 l 177.387 480.134 m 180.737 483.483 l 177.201 480.134 m 180.737 483.67 l 177.014 480.134 m 180.737 483.856 l 176.832 480.134 m 180.737 484.038 l 176.645 480.134 m 180.737 484.225 l 176.459 480.134 m 180.737 484.412 l 176.277 480.134 m 180.737 484.594 l 176.09 480.134 m 180.737 484.78 l 175.904 480.134 m 180.737 484.967 l 175.717 480.134 m 180.737 485.153 l 175.535 480.134 m 180.737 485.336 l 175.348 480.134 m 180.737 485.521 l 175.162 480.134 m 180.737 485.709 l 174.975 480.134 m 180.737 485.895 l 174.793 480.134 m 180.737 486.077 l 174.607 480.134 m 180.737 486.263 l 174.42 480.134 m 180.737 486.45 l 174.238 480.134 m 180.737 486.633 l 174.052 480.134 m 180.737 486.819 l 173.865 480.134 m 180.737 487.006 l 173.678 480.134 m 180.737 487.192 l 173.496 480.134 m 180.737 487.374 l 173.309 480.134 m 180.737 487.56 l 173.123 480.134 m 180.737 487.748 l 172.936 480.134 m 180.737 487.934 l 172.754 480.134 m 180.737 488.116 l 172.568 480.134 m 180.737 488.303 l 172.381 480.134 m 180.737 488.489 l 172.199 480.134 m 180.737 488.671 l 172.012 480.134 m 180.737 488.857 l 171.826 480.134 m 180.737 489.045 l 171.639 480.134 m 180.737 489.231 l 171.457 480.134 m 180.737 489.413 l 171.271 480.134 m 180.737 489.599 l 171.084 480.134 m 180.737 489.786 l 170.898 480.134 m 180.737 489.972 l 170.716 480.134 m 180.737 490.155 l 170.529 480.134 m 180.737 490.342 l 170.342 480.134 m 180.737 490.528 l 170.16 480.134 m 180.737 490.71 l 170.088 480.247 m 180.737 490.896 l 170.088 480.434 m 180.737 491.084 l 170.088 480.621 m 180.737 491.269 l 170.088 480.803 m 180.737 491.452 l 170.088 480.989 m 180.737 491.638 l 170.088 481.176 m 180.737 491.825 l 170.088 481.362 m 180.737 492.011 l 170.088 481.545 m 180.737 492.193 l 170.088 481.731 m 180.737 492.38 l 170.088 481.918 m 180.737 492.567 l 170.088 482.104 m 180.737 492.754 l 170.088 482.286 m 180.737 492.935 l 170.088 482.473 m 180.737 493.122 l 170.088 482.659 m 180.737 493.308 l 170.088 482.842 m 180.737 493.491 l 170.088 483.028 m 180.737 493.678 l 170.088 483.215 m 180.737 493.864 l 170.088 483.401 m 180.737 494.051 l 170.088 483.583 m 180.737 494.232 l 170.088 483.77 m 180.737 494.42 l 170.088 483.957 m 180.737 494.605 l 170.088 484.143 m 180.737 494.792 l 170.088 484.325 m 180.737 494.974 l 170.088 484.511 m 180.737 495.161 l 170.088 484.698 m 180.737 495.347 l 170.088 484.88 m 180.737 495.529 l 170.088 485.066 m 180.737 495.717 l 170.088 485.254 m 180.737 495.903 l 170.088 485.44 m 180.737 496.09 l 170.088 485.622 m 180.737 496.271 l 170.088 485.808 m 180.737 496.458 l 170.088 485.995 m 180.737 496.644 l 170.088 486.181 m 180.737 496.831 l 170.088 486.364 m 180.737 497.012 l 170.088 486.551 m 180.737 497.2 l 170.088 486.737 m 180.737 497.387 l 170.088 486.919 m 180.737 497.568 l 170.088 487.105 m 180.737 497.755 l 170.088 487.293 m 180.737 497.941 l 170.088 487.479 m 180.737 498.128 l 170.088 487.661 m 180.737 498.31 l 170.088 487.847 m 180.737 498.497 l 170.088 488.034 m 180.737 498.683 l 170.088 488.221 m 180.737 498.87 l 170.088 488.402 m 180.737 499.052 l 170.088 488.59 m 180.737 499.239 l 170.088 488.776 m 180.737 499.426 l 170.088 488.963 m 180.737 499.611 l 170.088 489.144 m 180.737 499.794 l 170.088 489.331 m 180.737 499.98 l 170.088 489.517 m 180.737 500.167 l 170.088 489.7 m 180.737 500.348 l 170.088 489.887 m 180.737 500.536 l 170.088 490.073 m 180.737 500.722 l 170.088 490.26 m 180.737 500.909 l 170.088 490.441 m 180.737 501.091 l 170.088 490.629 m 180.737 501.277 l 170.088 490.815 m 180.737 501.464 l 170.088 491.001 m 180.737 501.65 l 170.088 491.183 m 180.737 501.833 l 170.088 491.37 m 180.737 502.019 l 170.088 491.556 m 180.737 502.206 l 170.088 491.738 m 180.737 502.387 l 170.088 491.926 m 180.737 502.575 l 170.088 492.112 m 180.737 502.761 l 170.088 492.299 m 180.737 502.947 l 170.088 492.48 m 180.737 503.13 l 170.088 492.667 m 180.737 503.316 l 170.088 492.853 m 180.737 503.503 l 170.088 493.04 m 180.737 503.689 l 170.088 493.222 m 180.737 503.871 l 170.088 493.409 m 180.737 504.058 l 170.088 493.595 m 180.737 504.245 l 170.088 493.777 m 180.737 504.427 l 170.088 493.965 m 180.737 504.613 l 170.088 494.15 m 180.737 504.8 l 170.088 494.337 m 180.737 504.986 l 170.088 494.519 m 180.737 505.168 l 170.088 494.706 m 180.737 505.355 l 170.088 494.892 m 180.737 505.542 l 170.088 495.079 m 180.737 505.728 l 170.088 495.261 m 180.737 505.91 l 170.088 495.448 m 180.737 506.096 l 170.088 495.635 m 180.737 506.283 l 170.088 495.816 m 180.737 506.466 l 170.088 496.003 m 180.737 506.652 l 170.088 496.189 m 180.737 506.839 l 170.088 496.376 m 180.737 507.025 l 170.088 496.557 m 180.737 507.207 l 170.088 496.745 m 180.737 507.394 l 170.088 496.931 m 180.737 507.581 l 170.088 497.118 m 180.737 507.766 l 170.088 497.3 m 180.737 507.949 l 170.088 497.486 m 180.737 508.136 l 170.088 497.673 m 180.737 508.322 l 170.088 497.859 m 180.737 508.509 l 170.088 498.042 m 180.737 508.691 l 170.088 498.228 m 180.737 508.878 l 170.088 498.415 m 180.737 509.064 l 170.088 498.596 m 180.737 509.246 l 170.088 498.784 m 180.737 509.432 l 170.088 498.971 m 180.737 509.619 l 170.088 499.156 m 180.737 509.805 l 170.088 499.339 m 180.737 509.988 l 170.088 499.525 m 180.737 510.175 l 170.088 499.712 m 180.737 510.361 l 170.088 499.898 m 180.737 510.548 l 170.088 500.081 m 180.737 510.73 l 170.088 500.267 m 180.737 510.917 l 170.088 500.454 m 180.737 511.102 l 170.088 500.636 m 180.737 511.285 l 170.088 500.822 m 180.737 511.471 l 170.088 501.009 m 180.737 511.658 l 170.088 501.195 m 180.737 511.845 l 170.088 501.378 m 180.737 512.027 l 170.088 501.564 m 180.737 512.214 l 170.088 501.751 m 180.737 512.4 l 170.088 501.937 m 180.737 512.587 l 170.088 502.119 m 180.737 512.768 l 170.088 502.305 m 180.737 512.955 l 170.088 502.492 m 180.737 513.141 l 170.088 502.675 m 180.737 513.324 l 170.088 502.861 m 180.737 513.51 l 170.088 503.048 m 180.737 513.697 l 170.088 503.234 m 180.737 513.884 l 170.088 503.416 m 180.737 514.065 l 170.088 503.603 m 180.737 514.252 l 170.088 503.79 m 180.737 514.437 l 170.088 503.976 m 180.737 514.625 l 170.088 504.158 m 180.737 514.807 l 170.088 504.345 m 180.737 514.994 l 170.088 504.531 m 180.737 515.18 l 170.088 504.718 m 180.737 515.367 l 170.088 504.9 m 180.737 515.55 l 170.088 505.087 m 180.737 515.736 l 170.088 505.273 m 180.737 515.923 l 170.088 505.455 m 180.737 516.104 l 170.088 505.641 m 180.737 516.291 l 170.088 505.828 m 180.737 516.477 l 170.088 506.014 m 180.737 516.664 l 170.088 506.197 m 180.737 516.846 l 170.088 506.384 m 180.737 517.033 l 170.088 506.57 m 180.737 517.22 l 170.088 506.757 m 180.737 517.406 l 170.088 506.939 m 180.737 517.588 l 170.088 507.126 m 180.737 517.774 l 170.088 507.311 m 180.737 517.961 l 170.088 507.494 m 180.737 518.143 l 170.088 507.68 m 180.737 518.33 l 170.088 507.867 m 180.737 518.516 l S 180.91 480.134 m 191.385 490.609 l 180.737 480.147 m 191.385 490.797 l 180.737 480.334 m 191.385 490.983 l 180.737 480.515 m 191.385 491.165 l 180.737 480.702 m 191.385 491.351 l 180.737 480.889 m 191.385 491.539 l 180.737 481.076 m 191.385 491.724 l 180.737 481.258 m 191.385 491.907 l 180.737 481.444 m 191.385 492.094 l 180.737 481.631 m 191.385 492.28 l 180.737 481.813 m 191.385 492.462 l 180.737 482 m 191.385 492.648 l 180.737 482.186 m 191.385 492.836 l 180.737 482.373 m 191.385 493.022 l 180.737 482.554 m 191.385 493.204 l 180.737 482.741 m 191.385 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191.385 508.959 l 180.737 498.497 m 191.385 509.146 l 180.737 498.683 m 191.385 509.333 l 180.737 498.87 m 191.385 509.519 l 180.737 499.052 m 191.385 509.701 l 180.737 499.239 m 191.385 509.887 l 180.737 499.426 m 191.385 510.074 l 180.737 499.611 m 191.385 510.261 l 180.737 499.794 m 191.385 510.443 l 180.737 499.98 m 191.385 510.63 l 180.737 500.167 m 191.385 510.816 l 180.737 500.348 m 191.385 510.998 l 180.737 500.536 m 191.385 511.185 l 180.737 500.722 m 191.385 511.372 l 180.737 500.909 m 191.385 511.557 l 180.737 501.091 m 191.385 511.74 l 180.737 501.277 m 191.385 511.927 l 180.737 501.464 m 191.385 512.113 l 180.737 501.65 m 191.385 512.3 l 180.737 501.833 m 191.385 512.482 l 180.737 502.019 m 191.385 512.669 l 180.737 502.206 m 191.385 512.855 l 180.737 502.387 m 191.385 513.037 l 180.737 502.575 m 191.385 513.223 l 180.737 502.761 m 191.385 513.41 l 180.737 502.947 m 191.385 513.596 l 180.737 503.13 m 191.385 513.779 l 180.737 503.316 m 191.385 513.966 l 180.737 503.503 m 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m 187.422 515.377 l 180.737 508.878 m 187.235 515.377 l 180.737 509.064 m 187.049 515.377 l 180.737 509.246 m 186.862 515.377 l 180.737 509.432 m 186.68 515.377 l 180.737 509.619 m 186.494 515.377 l 180.737 509.805 m 186.307 515.377 l 180.737 509.988 m 186.125 515.377 l 180.737 510.175 m 185.938 515.377 l 180.737 510.361 m 185.752 515.377 l 180.737 510.548 m 185.565 515.377 l 180.737 510.73 m 185.383 515.377 l 180.737 510.917 m 185.197 515.377 l 180.737 511.102 m 185.01 515.377 l 180.737 511.285 m 184.824 515.377 l 180.737 511.471 m 184.641 515.377 l 180.737 511.658 m 184.455 515.377 l 180.737 511.845 m 184.268 515.377 l 180.737 512.027 m 184.082 515.377 l 180.737 512.214 m 183.899 515.377 l 180.737 512.4 m 183.713 515.377 l 180.737 512.587 m 183.527 515.377 l 180.737 512.768 m 183.344 515.377 l 180.737 512.955 m 183.158 515.377 l 180.737 513.141 m 182.971 515.377 l 180.737 513.324 m 182.785 515.377 l 180.737 513.51 m 182.602 515.377 l 180.737 513.697 m 182.416 515.377 l 180.737 513.884 m 182.229 515.377 l 180.737 514.065 m 182.043 515.377 l 180.737 514.252 m 181.86 515.377 l 180.737 514.437 m 181.675 515.377 l 180.737 514.625 m 181.488 515.377 l 180.737 514.807 m 181.305 515.377 l 180.737 514.994 m 181.119 515.377 l 180.737 515.18 m 180.932 515.377 l 180.737 515.367 m 180.746 515.377 l 180.722 480.134 m 180.737 480.147 l 180.537 480.134 m 180.737 480.334 l 180.354 480.134 m 180.737 480.515 l 180.168 480.134 m 180.737 480.702 l 179.981 480.134 m 180.737 480.889 l 179.795 480.134 m 180.737 481.076 l 179.613 480.134 m 180.737 481.258 l 179.426 480.134 m 180.737 481.444 l S 197.589 480.134 m 202.035 484.58 l 197.407 480.134 m 202.035 484.761 l 197.22 480.134 m 202.035 484.948 l 197.034 480.134 m 202.035 485.136 l 196.851 480.134 m 202.035 485.317 l 196.665 480.134 m 202.035 485.504 l 196.478 480.134 m 202.035 485.69 l 196.292 480.134 m 202.035 485.877 l 196.11 480.134 m 202.035 486.059 l 195.924 480.134 m 202.035 486.246 l 195.736 480.134 m 202.035 486.432 l 195.551 480.134 m 202.035 486.619 l 195.368 480.134 m 202.035 486.801 l 195.181 480.134 m 202.035 486.987 l 194.995 480.134 m 202.035 487.174 l 194.813 480.134 m 202.035 487.356 l 194.627 480.134 m 202.035 487.543 l 194.439 480.134 m 202.035 487.729 l 194.253 480.134 m 202.035 487.916 l 194.071 480.134 m 202.035 488.097 l 193.884 480.134 m 202.035 488.284 l 193.698 480.134 m 202.035 488.471 l 193.511 480.134 m 202.035 488.658 l 193.329 480.134 m 202.035 488.84 l 193.142 480.134 m 202.035 489.026 l 192.956 480.134 m 202.035 489.213 l 192.769 480.134 m 202.035 489.399 l 192.588 480.134 m 202.035 489.581 l 192.401 480.134 m 202.035 489.767 l 192.215 480.134 m 202.035 489.955 l 192.032 480.134 m 202.035 490.137 l 191.845 480.134 m 202.035 490.323 l 191.659 480.134 m 202.035 490.51 l 191.472 480.134 m 202.035 490.696 l 191.385 480.229 m 202.035 490.879 l 191.385 480.416 m 202.035 491.065 l 191.385 480.602 m 202.035 491.252 l 191.385 480.789 m 202.035 491.438 l 191.385 480.971 m 202.035 491.62 l 191.385 481.157 m 202.035 491.806 l 191.385 481.345 m 202.035 491.994 l 191.385 481.526 m 202.035 492.176 l 191.385 481.713 m 202.035 492.362 l 191.385 481.899 m 202.035 492.549 l 191.385 482.086 m 202.035 492.735 l 191.385 482.268 m 202.035 492.917 l 191.385 482.455 m 202.035 493.103 l 191.385 482.641 m 202.035 493.291 l 191.385 482.828 m 202.035 493.477 l 191.385 483.01 m 202.035 493.659 l 191.385 483.196 m 202.035 493.845 l 191.385 483.384 m 202.035 494.032 l 191.385 483.565 m 202.035 494.215 l 191.385 483.752 m 202.035 494.401 l 191.385 483.938 m 202.035 494.588 l 191.385 484.125 m 202.035 494.774 l 191.385 484.306 m 202.035 494.956 l 191.385 484.493 m 202.035 495.142 l 191.385 484.68 m 202.035 495.33 l 191.385 484.867 m 202.035 495.515 l 191.385 485.049 m 202.035 495.698 l 191.385 485.235 m 202.035 495.885 l 191.385 485.422 m 202.035 496.071 l 191.385 485.608 m 202.035 496.258 l 191.385 485.791 m 202.035 496.439 l 191.385 485.977 m 202.035 496.627 l 191.385 486.164 m 202.035 496.813 l 191.385 486.345 m 202.035 496.995 l 191.385 486.532 m 202.035 497.181 l 191.385 486.719 m 202.035 497.368 l 191.385 486.905 m 202.035 497.554 l 191.385 487.088 m 202.035 497.737 l 191.385 487.274 m 202.035 497.924 l 191.385 487.461 m 202.035 498.11 l 191.385 487.647 m 202.035 498.297 l 191.385 487.828 m 202.035 498.478 l 191.385 488.015 m 202.035 498.666 l 191.385 488.203 m 202.035 498.851 l 191.385 488.385 m 202.035 499.034 l 191.385 488.571 m 202.035 499.221 l 191.385 488.758 m 202.035 499.407 l 191.385 488.944 m 202.035 499.594 l 191.385 489.126 m 202.035 499.775 l 191.385 489.312 m 202.035 499.962 l 191.385 489.5 m 202.035 500.149 l 191.385 489.686 m 202.035 500.336 l 191.385 489.868 m 202.035 500.517 l 191.385 490.054 m 201.912 500.581 l 191.385 490.241 m 201.725 500.581 l 191.385 490.424 m 201.544 500.581 l 191.385 490.609 m 201.357 500.581 l 191.385 490.797 m 201.171 500.581 l 191.385 490.983 m 200.984 500.581 l 191.385 491.165 m 200.802 500.581 l 191.385 491.351 m 200.615 500.581 l 191.385 491.539 m 200.428 500.581 l 191.385 491.724 m 200.242 500.581 l 191.385 491.907 m 200.06 500.581 l 191.385 492.094 m 199.874 500.581 l 191.385 492.28 m 199.687 500.581 l 191.385 492.462 m 199.505 500.581 l 191.385 492.648 m 199.318 500.581 l 191.385 492.836 m 199.132 500.581 l 191.385 493.022 m 198.945 500.581 l 191.385 493.204 m 198.763 500.581 l 191.385 493.39 m 198.576 500.581 l 191.385 493.577 m 198.389 500.581 l 191.385 493.763 m 198.204 500.581 l 191.385 493.946 m 198.021 500.581 l 191.385 494.133 m 197.835 500.581 l 191.385 494.319 m 197.648 500.581 l 191.385 494.506 m 197.467 500.581 l 191.385 494.687 m 197.279 500.581 l 191.385 494.875 m 197.093 500.581 l 191.385 495.06 m 196.906 500.581 l 191.385 495.243 m 196.724 500.581 l 191.385 495.429 m 196.538 500.581 l 191.385 495.616 m 196.351 500.581 l 191.385 495.803 m 196.165 500.581 l 191.385 495.984 m 195.982 500.581 l 191.385 496.172 m 195.796 500.581 l 191.385 496.358 m 195.609 500.581 l 191.385 496.545 m 195.427 500.581 l 191.385 496.726 m 195.24 500.581 l 191.385 496.913 m 195.053 500.581 l 191.385 497.099 m 194.868 500.581 l 191.385 497.282 m 194.685 500.581 l 191.385 497.468 m 194.499 500.581 l 191.385 497.655 m 194.312 500.581 l 191.385 497.842 m 194.126 500.581 l 191.385 498.023 m 193.944 500.581 l 191.385 498.21 m 193.757 500.581 l 191.385 498.396 m 193.57 500.581 l 191.385 498.583 m 193.388 500.581 l 191.385 498.765 m 193.202 500.581 l 191.385 498.952 m 193.015 500.581 l 191.385 499.138 m 192.829 500.581 l 191.385 499.32 m 192.646 500.581 l 191.385 499.507 m 192.46 500.581 l 191.385 499.694 m 192.273 500.581 l 191.385 499.881 m 192.087 500.581 l 191.385 500.062 m 191.905 500.581 l 191.385 500.249 m 191.718 500.581 l 191.385 500.435 m 191.532 500.581 l 191.291 480.134 m 191.385 480.229 l 191.103 480.134 m 191.385 480.416 l 190.917 480.134 m 191.385 480.602 l 190.73 480.134 m 191.385 480.789 l 190.549 480.134 m 191.385 480.971 l 190.362 480.134 m 191.385 481.157 l 190.176 480.134 m 191.385 481.345 l 189.994 480.134 m 191.385 481.526 l 189.806 480.134 m 191.385 481.713 l 189.62 480.134 m 191.385 481.899 l 189.433 480.134 m 191.385 482.086 l 189.252 480.134 m 191.385 482.268 l 189.065 480.134 m 191.385 482.455 l 188.879 480.134 m 191.385 482.641 l 188.692 480.134 m 191.385 482.828 l 188.51 480.134 m 191.385 483.01 l 188.323 480.134 m 191.385 483.196 l 188.136 480.134 m 191.385 483.384 l 187.955 480.134 m 191.385 483.565 l 187.768 480.134 m 191.385 483.752 l 187.581 480.134 m 191.385 483.938 l 187.395 480.134 m 191.385 484.125 l 187.213 480.134 m 191.385 484.306 l 187.026 480.134 m 191.385 484.493 l 186.84 480.134 m 191.385 484.68 l 186.653 480.134 m 191.385 484.867 l 186.471 480.134 m 191.385 485.049 l 186.284 480.134 m 191.385 485.235 l 186.097 480.134 m 191.385 485.422 l 185.911 480.134 m 191.385 485.608 l 185.729 480.134 m 191.385 485.791 l 185.543 480.134 m 191.385 485.977 l 185.356 480.134 m 191.385 486.164 l 185.174 480.134 m 191.385 486.345 l 184.987 480.134 m 191.385 486.532 l 184.801 480.134 m 191.385 486.719 l 184.614 480.134 m 191.385 486.905 l 184.432 480.134 m 191.385 487.088 l 184.245 480.134 m 191.385 487.274 l 184.059 480.134 m 191.385 487.461 l 183.873 480.134 m 191.385 487.647 l 183.69 480.134 m 191.385 487.828 l 183.504 480.134 m 191.385 488.015 l 183.317 480.134 m 191.385 488.203 l 183.135 480.134 m 191.385 488.385 l 182.949 480.134 m 191.385 488.571 l 182.761 480.134 m 191.385 488.758 l 182.575 480.134 m 191.385 488.944 l 182.393 480.134 m 191.385 489.126 l 182.207 480.134 m 191.385 489.312 l 182.02 480.134 m 191.385 489.5 l 181.834 480.134 m 191.385 489.686 l 181.652 480.134 m 191.385 489.868 l 181.465 480.134 m 191.385 490.054 l 181.278 480.134 m 191.385 490.241 l 181.096 480.134 m 191.385 490.424 l S 223.724 480.134 m 223.834 480.238 l 223.543 480.134 m 223.647 480.238 l 223.356 480.134 m 223.462 480.238 l 223.17 480.134 m 223.334 480.298 l 222.983 480.134 m 223.334 480.484 l 222.802 480.134 m 223.334 480.666 l 222.615 480.134 m 223.334 480.852 l 222.427 480.134 m 223.334 481.039 l 222.241 480.134 m 223.334 481.226 l 222.059 480.134 m 223.334 481.408 l 221.873 480.134 m 223.334 481.595 l 221.686 480.134 m 223.334 481.781 l 221.504 480.134 m 223.334 481.964 l 221.317 480.134 m 223.166 481.981 l 221.132 480.134 m 222.978 481.981 l 220.944 480.134 m 222.797 481.981 l 220.762 480.134 m 222.61 481.981 l 220.576 480.134 m 222.424 481.981 l 220.389 480.134 m 222.241 481.981 l 220.203 480.134 m 222.054 481.981 l 220.02 480.134 m 221.869 481.981 l 219.834 480.134 m 221.681 481.981 l 219.647 480.134 m 221.5 481.981 l 219.466 480.134 m 221.313 481.981 l 219.279 480.134 m 221.127 481.981 l 219.093 480.134 m 220.94 481.981 l 218.905 480.134 m 220.758 481.981 l 218.723 480.134 m 220.571 481.981 l 218.537 480.134 m 220.384 481.981 l 218.35 480.134 m 220.198 481.981 l 218.164 480.134 m 220.016 481.981 l 217.982 480.134 m 219.83 481.981 l 217.796 480.134 m 219.642 481.981 l 217.608 480.134 m 219.461 481.981 l 217.422 480.134 m 219.274 481.981 l 217.24 480.134 m 219.088 481.981 l 217.053 480.134 m 218.901 481.981 l 216.867 480.134 m 218.718 481.981 l 216.684 480.134 m 218.533 481.981 l 216.498 480.134 m 218.345 481.981 l 216.311 480.134 m 218.159 481.981 l 216.125 480.134 m 217.977 481.981 l 215.943 480.134 m 217.791 481.981 l 215.757 480.134 m 217.604 481.981 l 215.57 480.134 m 217.422 481.981 l 215.384 480.134 m 217.235 481.981 l 215.201 480.134 m 217.049 481.981 l 215.014 480.134 m 216.862 481.981 l 214.828 480.134 m 216.68 481.981 l 214.646 480.134 m 216.494 481.981 l 214.46 480.134 m 216.306 481.981 l 214.273 480.134 m 216.12 481.981 l 214.086 480.134 m 215.938 481.981 l 213.904 480.134 m 215.752 481.981 l 213.718 480.134 m 215.565 481.981 l 213.531 480.134 m 215.384 481.981 l 213.344 480.134 m 215.197 481.981 l 213.162 480.134 m 215.01 481.981 l 212.976 480.134 m 214.823 481.981 l 212.789 480.134 m 214.641 481.981 l 212.684 480.211 m 214.455 481.981 l 212.684 480.397 m 214.268 481.981 l 212.684 480.584 m 214.082 481.981 l 212.684 480.771 m 213.899 481.981 l 212.684 480.953 m 213.713 481.981 l 212.684 481.138 m 213.526 481.981 l 212.684 481.326 m 213.34 481.981 l 212.684 481.512 m 213.158 481.981 l 212.684 481.695 m 212.971 481.981 l 212.684 481.88 m 212.784 481.981 l 212.607 480.134 m 212.684 480.211 l 212.421 480.134 m 212.684 480.397 l 212.234 480.134 m 212.684 480.584 l 212.048 480.134 m 212.684 480.771 l 211.865 480.134 m 212.684 480.953 l 211.678 480.134 m 212.684 481.138 l 211.492 480.134 m 212.684 481.326 l 211.305 480.134 m 212.684 481.512 l 211.124 480.134 m 212.684 481.695 l 210.937 480.134 m 212.684 481.88 l 210.75 480.134 m 212.684 482.068 l 210.563 480.134 m 212.684 482.255 l 210.382 480.134 m 212.684 482.436 l 210.195 480.134 m 212.684 482.623 l 210.009 480.134 m 212.684 482.809 l 209.826 480.134 m 212.684 482.992 l 209.64 480.134 m 212.684 483.179 l 209.453 480.134 m 212.684 483.365 l 209.266 480.134 m 212.684 483.552 l 209.085 480.134 m 212.684 483.733 l 208.898 480.134 m 212.684 483.92 l 208.712 480.134 m 212.684 484.107 l 208.525 480.134 m 212.684 484.294 l 208.343 480.134 m 212.684 484.475 l 208.156 480.134 m 212.684 484.661 l 207.969 480.134 m 212.684 484.848 l 207.788 480.134 m 212.684 485.03 l 207.601 480.134 m 212.684 485.217 l 207.414 480.134 m 212.684 485.403 l 207.227 480.134 m 212.684 485.591 l 207.046 480.134 m 212.684 485.772 l 206.859 480.134 m 212.684 485.959 l 206.673 480.134 m 212.684 486.145 l 206.486 480.134 m 212.684 486.332 l 206.304 480.134 m 212.684 486.514 l 206.117 480.134 m 212.684 486.701 l 205.93 480.134 m 212.684 486.887 l 205.749 480.134 m 212.684 487.069 l 205.562 480.134 m 212.684 487.256 l 205.376 480.134 m 212.684 487.442 l 205.189 480.134 m 212.684 487.629 l 205.007 480.134 m 212.684 487.811 l 204.82 480.134 m 212.684 487.998 l 204.634 480.134 m 212.684 488.184 l 204.447 480.134 m 212.684 488.371 l 204.265 480.134 m 212.684 488.553 l 204.079 480.134 m 212.684 488.739 l 203.892 480.134 m 212.684 488.927 l 203.71 480.134 m 212.684 489.108 l 203.523 480.134 m 212.662 489.276 l 203.337 480.134 m 212.479 489.276 l 203.15 480.134 m 212.294 489.276 l 202.968 480.134 m 212.106 489.276 l 202.782 480.134 m 211.92 489.276 l 202.594 480.134 m 211.738 489.276 l 202.408 480.134 m 211.551 489.276 l 202.226 480.134 m 211.365 489.276 l 202.04 480.134 m 211.178 489.276 l 202.035 480.316 m 210.996 489.276 l 202.035 480.503 m 210.809 489.276 l 202.035 480.684 m 210.623 489.276 l 202.035 480.87 m 210.441 489.276 l 202.035 481.057 m 210.255 489.276 l 202.035 481.24 m 210.067 489.276 l 202.035 481.426 m 209.881 489.276 l 202.035 481.613 m 209.699 489.276 l 202.035 481.8 m 209.512 489.276 l 202.035 481.981 m 209.326 489.276 l 202.035 482.168 m 209.139 489.276 l 202.035 482.354 m 208.958 489.276 l 202.035 482.541 m 208.77 489.276 l 202.035 482.723 m 208.584 489.276 l 202.035 482.91 m 208.402 489.276 l 202.035 483.096 m 208.216 489.276 l 202.035 483.278 m 208.029 489.276 l 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(\003)Tj /T1_2 1 Tf 1.345 0 Td (\001)Tj /T1_3 1 Tf 0.687 0 Td (\003)Tj /T1_4 1 Tf 0.005 Tc 0.418 0 Td (mean)Tj /T1_5 1 Tf 0 Tc 2.598 0 Td (\001)Tj /T1_4 1 Tf 0.005 Tc 1.14 0 Td [(4)-80(,)-415(var)]TJ /T1_5 1 Tf 0 Tc 2.821 0 Td (\001)Tj /T1_4 1 Tf 0.0849 Tc 1.14 0 Td (16)Tj /T1_3 1 Tf 0 Tc 1.17 0 Td (\004)Tj /T1_4 1 Tf 0.418 0 Td (.)Tj 0.005 Tc -20.159 -2.004 Td [(Here,)-253(the)-253(hyperparameters)-253(on)-253(the)-253(fat)-30(alit)-30(y)-253(rate)-253(are)]TJ /T1_0 1 Tf 0 Tc 21.824 0 Td (a)Tj 6.5 0 0 6 252.7144 695.7699 Tm (e)Tj /T1_4 1 Tf 9 0 0 9 255.5277 697.0199 Tm (,)Tj /T1_0 1 Tf 0.508 0 Td (b)Tj 6.5 0 0 6 264.7041 695.7699 Tm (e)Tj /T1_4 1 Tf 9 0 0 9 267.5175 697.0199 Tm (,)Tj /T1_0 1 Tf 0.508 0 Td (a)Tj 6.5 0 0 6 276.7118 695.7699 Tm (u)Tj /T1_4 1 Tf 0.005 Tc 9 0 0 9 280.2662 697.0199 Tm [(,)-253(and)]TJ /T1_0 1 Tf 0 Tc -25.399 -1.111 Td (b)Tj 6.5 0 0 6 56.2844 685.7699 Tm (u)Tj /T1_4 1 Tf 0.005 Tc 9 0 0 9 59.8388 687.0199 Tm [(,)-455(and)]TJ /T1_2 1 Tf 0 Tc 2.769 0 Td (\001)Tj /T1_4 1 Tf 0.672 0 Td (,)Tj /T1_6 1 Tf 0.005 Tc 0.71 0 Td (LN)Tj /T1_4 1 Tf 1.38 0 Td [(,)-455(and)]TJ /T1_6 1 Tf 2.769 0 Td (Be)Tj /T1_4 1 Tf 1.572 0 Td [(denote)-455(gamma,)-455(log-nor)-30(mal,)-455(and)-455(bet)-30(a)]TJ -10.778 -1.111 Td [(distributions,)-544(re)20(spectively.)-544(Note)-544(that)]TJ /T1_0 1 Tf 0 Tc 17.004 0 Td (e)Tj /T1_4 1 Tf 0.005 Tc 0.977 0 Td [(st)-30(ands)-544(for)-544(prev)-40(iously)]TJ -17.981 -1.111 Td [(ex)-30(posed)-220(Old)-220(World)-220(populations,)-220(whereas)]TJ /T1_0 1 Tf 0 Tc 17.859 0 Td (u)Tj /T1_4 1 Tf 0.005 Tc 0.767 0 Td [(st)-30(ands)-220(for)-220(prev)-40(iously)]TJ -18.626 -1.111 Td [(unex)-30(posed)-338(New)-338(World)-338(populations.)]TJ /T1_7 1 Tf 0 Tc 8 0 0 8 51.6761 637.0199 Tm [(Likelihood)-279(Calculation.)]TJ /T1_4 1 Tf 0.0199 Tc 9 0 0 9 135.5705 637.0199 Tm [(In)-248(fitting)-248(the)-248(SEIR)-248(model,)-248(we)-248(c)-30(onsidered)]TJ -9.322 -1.111 Td [(only)-519(epidemic)-519(dat)-30(a)-519(because)-519(of)-519(the)-519(dif)-30(ficult)-30(y)-519(of)-519(fitting)-519(the)]TJ 0 -1.111 TD [(c)-30(omplex)-206(f)-90(luctuations)-206(t)-30(ypical)-206(of)-206(endemic)-206(dat)-30(a)-206(\(10,)-206(18\).)-206(A)-30(lso,)-206(we)]TJ T* [(used)-300(only)-300(18th)-300(and)-300(19th)-300(centur)-60(y)-300(epidemics)-300(\(Table)-300(3\))-300(to)-300(avoid)]TJ T* [(the)-317(c)-30(omplication)-317(of)-317(vac)-30(cination.)-317(In)-317(using)-317(epidemic)-317(dat)-30(a)-317(f)-30(rom)]TJ 0 -1.111 TD [(prev)-40(ious)-245(centurie)20(s,)-245(we)-245(are)-245(implicitly)-245(assuming)-245(that)-245(parameters)]TJ T* [(e)20(stimated)-343(f)-30(rom)-343(such)-343(dat)-30(a)-343(are)-343(relevant)-343(to)-343(c)-30(ontemporar)-60(y)-343(pop-)]TJ T* [(ulations.)-516(Given)-516(that)]TJ /T1_0 1 Tf 0 Tc 9.818 0 Td (R)Tj /T1_4 1 Tf 6.5 0 0 6 146.2547 565.7699 Tm (0)Tj 0.0199 Tc 9 0 0 9 154.2832 567.0199 Tm [(in)-516(particular)-516(is)-516(likely)-516(to)-516(var)-60(y)-516(in)-516(a)]TJ -11.401 -1.111 Td [(c)-30(omplex)-195(way)-195(across)-195(centurie)20(s,)-195(because,)-195(for)-195(example,)-195(of)-195(change)20(s)]TJ 0 -1.111 TD [(in)-334(social)-334(mix)-50(ing)-334(or)-334(ac)-30(ce)20(ss)-334(to)-334(infor)-30(mation)-334(regarding)-334(smallpox,)]TJ T* [(it)-201(is)-201(likely)-201(that,)-201(in)-201(fact,)-201(smallpox)-201(spread)-201(rate)20(s)-201(would)-201(be)-201(dif)-30(ferent)]TJ T* [(in)-314(c)-30(ontemporar)-60(y)-314(populations.)-314(Neverthele)20(ss,)-314(as)-314(we)-314(de)20(scribe)-314(in)]TJ /T1_0 1 Tf 0 -1.111 TD [(Results)-365(and)-365(Discussion)]TJ /T1_4 1 Tf 10.065 0 Td [(,)-365(allow)-40(ing)-365(for)-365(dif)-30(ference)20(s)-365(bet)-30(ween)-365(his-)]TJ -10.065 -1.111 Td [(torical)-322(and)-322(c)-30(ontemporar)-60(y)-322(populations)-322(almost)-322(cert)-30(ainly)-322(would)]TJ T* [(increase)-254(the)-254(uncert)-30(aint)-30(y)-254(in)-254(the)-254(parameters,)-254(reemphasizing)-254(our)]TJ T* [(main)-301(point.)-301(Moreover,)-301(in)-301(using)-301(historical)-301(dat)-30(a,)-301(we)-301(are)-301(follow-)]TJ T* [(ing)-407(e)20(ssentially)-407(all)-407(prev)-40(ious)-407(smallpox)-407(modeling)-407(studie)20(s;)-407(given)]TJ T* [(that)-317(our)-317(goal)-317(is)-317(to)-317(sugge)20(st)-317(a)-317(modification)-317(to)-317(the)-317(methodolog)-40(y)]TJ T* [(of)-353(such)-353(studie)20(s,)-353(using)-353(historical)-353(dat)-30(a)-353(is)-353(appropriate.)]TJ 0.005 Tc 1 -1.111 Td [(The)-338(likelihood)-338(is)-338(then)-338(based)-338(on)]TJ 0.0199 Tc 7.697 -2.022 Td [(Dat)-30(a)]TJ /T1_0 1 Tf 0.0329 Tc 6.3977 0 0 5.7614 150.0049 427.233 Tm (ij)Tj /T1_1 1 Tf 0 Tc 9 0 0 9 155.7685 428.8239 Tm (\003)Tj /T1_6 1 Tf 1.14 0 Td (N)Tj /T1_3 1 Tf 0.74 0 Td (\003)Tj /T1_4 1 Tf 0.005 Tc 0.418 0 Td (Dead)Tj /T1_0 1 Tf 0.0329 Tc 6.3977 0 0 5.7614 197.6978 427.233 Tm (ij)Tj /T1_4 1 Tf 0 Tc 9 0 0 9 201.4642 428.8239 Tm (,)Tj /T1_5 1 Tf 9 0 1.3977 9 207.4926 428.8239 Tm (\006)Tj /T1_0 1 Tf 6.3977 0 0 5.7614 213.7555 426.9375 Tm (I)Tj /T1_4 1 Tf 0 1 Td (2)Tj /T1_3 1 Tf 9 0 0 9 217.1674 428.8239 Tm (\004)Tj /T1_4 1 Tf 0.0199 Tc -9.891 -2.025 Td (Dead)Tj /T1_0 1 Tf 0.0329 Tc 6.3977 0 0 5.7614 149.9346 409.0057 Tm (ij)Tj /T1_5 1 Tf 0 Tc 9 0 0 9 155.6982 410.5966 Tm (\001)Tj 9 0 1.3977 9 165.9563 410.5966 Tm (\005)Tj /T1_0 1 Tf 6.3977 0 0 5.7614 172.7232 409.0057 Tm (I)Tj 9 0 0 9 176.2686 410.5966 Tm (f)Tj /T1_3 1 Tf 0.381 0 Td (\003)Tj /T1_0 1 Tf 0.418 0 Td (R)Tj /T1_4 1 Tf 0.0329 Tc 6.3977 0 0 5.7614 190.2608 409.0057 Tm (0,)Tj /T1_0 1 Tf 0 Tc 0.816 0 Td (I)Tj /T1_4 1 Tf 9 0 0 9 198.0249 410.5966 Tm (,)Tj /T1_5 1 Tf 9 0 1.3977 9 204.0532 410.5966 Tm (\004)Tj /T1_4 1 Tf 9 0 0 9 210.3162 410.5966 Tm (,)Tj /T1_5 1 Tf 9 0 1.3977 9 216.3445 410.5966 Tm (\002)Tj /T1_3 1 Tf 9 0 0 9 222.1125 410.5966 Tm (\004)Tj /T1_4 1 Tf 0.418 0 Td (.)Tj /T1_6 1 Tf 0.0199 Tc 6.726 1.111 Td ([4])Tj /T1_4 1 Tf 0.005 Tc -26.081 -3.115 Td [(Here,)-536(Dat)-30(a)]TJ /T1_0 1 Tf 0.0048 Tc 6.5 0 0 6 98.2112 391.3153 Tm (ij)Tj /T1_4 1 Tf 0.005 Tc 9 0 0 9 106.5 392.5653 Tm [(and)-536(Dead)]TJ /T1_0 1 Tf 0.0048 Tc 6.5 0 0 6 147.0044 391.3153 Tm (ij)Tj /T1_4 1 Tf 0.005 Tc 9 0 0 9 155.2933 392.5653 Tm [(are,)-536(re)20(spectively,)-536(the)-536(obser)-60(ved)-536(and)]TJ -11.513 -1.111 Td [(predicted)-267(number)-267(of)-267(indiv)-40(iduals)-267(who)-267(died)-267(in)-267(the)]TJ /T1_0 1 Tf 0 Tc 21.064 0 Td (i)Tj /T1_4 1 Tf 0.005 Tc 0.269 0 Td [(th)-267(epidemic)-267(at)]TJ -21.333 -1.111 Td (time)Tj /T1_0 1 Tf 0 Tc 2.248 0 Td (j)Tj /T1_4 1 Tf 0.005 Tc 0.264 0 Td [(,)-312(and)]TJ /T1_0 1 Tf 0 Tc 2.483 0 Td (f)Tj /T1_4 1 Tf 0.301 0 Td (\()Tj /T1_0 1 Tf 0.388 0 Td (R)Tj /T1_4 1 Tf 0.0048 Tc 6.5 0 0 6 108.9151 371.3153 Tm (0,)Tj /T1_0 1 Tf 0 Tc 0.76 0 Td (I)Tj /T1_4 1 Tf 9 0 0 9 116.2567 372.5653 Tm (,)Tj /T1_5 1 Tf 9 0 1.3977 9 121.3645 372.5653 Tm (\004)Tj /T1_4 1 Tf 9 0 0 9 126.9088 372.5653 Tm (,)Tj /T1_5 1 Tf 9 0 1.3977 9 132.0166 372.5653 Tm (\002)Tj /T1_4 1 Tf 0.005 Tc 9 0 0 9 137.0659 372.5653 Tm [(\))-312(is)-312(the)-312(model\222s)-312(prediction)-312(of)-312(the)-312(number)]TJ -9.488 -1.111 Td [(of)-561(indiv)-40(iduals)-561(rec)-30(overing)-561(and)-561(dying.)-561(Because)-561(of)-561(dif)-30(ference)20(s)]TJ 0 -1.111 TD [(bet)-30(ween)-414(Old)-414(World)-414(and)-414(New)-414(World)-414(populations,)-414(we)-414(allowed)]TJ T* [(some)-250(parameters)-250(to)-250(dif)-30(fer)-250(bet)-30(ween)-250(them)-250(\(15\),)-250(and)-250(so)]TJ /T1_0 1 Tf 0 Tc 23.089 0 Td (I)Tj /T1_4 1 Tf 0.005 Tc 0.62 0 Td [(indicate)20(s)]TJ -23.709 -1.111 Td [(whether)-254(a)-254(population)-254(is)-254(Old)-254(World)-254(or)-254(New)-254(World.)-254(Note)-254(that)-254(we)]TJ 0 -1.111 TD [(assume)-187(that)-187(the)-187(errors)-187(in)-187(the)-187(fit)-187(of)-187(the)-187(model)-187(to)-187(the)-187(epidemic)-187(dat)-30(a)]TJ 29.167 45.813 Td [(are)-199(nor)-30(mally)-199(distributed.)-199(Our)-199(reason)-30(ing)-199(for)-199(this)-199(choice)-199(is)-199(that)-199(the)]TJ 0 -1.123 TD [(population)-292(size)20(s)-292(in)-292(the)-292(epidemic)-292(dat)-30(a)-292(were)-292(in)-292(the)-292(hundreds;)-292(for)]TJ T* [(such)-194(sample)-194(size)20(s,)-194(a)-194(nor)-30(mal)-194(distribution)-194(t)-30(ypically)-194(prov)-40(ide)20(s)-194(a)-194(good)]TJ T* [(approx)-50(imation)-237(to)-237(a)-237(binomial)-237(distribution.)-237(Moreover,)-237(the)-237(nor)-30(mal)]TJ T* [(distribution)-435(is)-435(c)-30(omput)-30(ationally)-435(c)-30(onven)-30(ient,)-435(particularly)-435(in)-435(the)]TJ T* [(current)-562(Baye)20(sian)-562(c)-30(ontext.)-562(More)-562(generally,)-562(using)-562(a)-562(binomial)]TJ T* [(distribution)-225(would)-225(be)-225(equivalent)-225(to)-225(assuming)-225(that)-225(all)-225(of)-225(the)-225(error)]TJ T* [(in)-458(the)-458(fit)-458(of)-458(the)-458(model)-458(is)-458(simply)-458(binomial)-458(sampling)-458(error.)-458(A)]TJ 0 -1.122 TD [(nor)-30(mal)-209(distribution)-209(in)-209(c)-30(ontrast)-209(allows)-209(the)-209(magn)-30(itude)-209(of)-209(the)-209(error)]TJ T* [(to)-384(be)-384(independent)-384(of)-384(its)-384(mean)-384(size)-384(and,)-384(thus,)-384(is)-384(in)-384(this)-384(case)-384(a)]TJ T* [(c)-30(onser)-60(vative)-338(choice.)]TJ 1 -1.122 Td [(A)-30(n)-457(import)-30(ant)-457(feature)-457(of)-457(our)-457(likelihood)-457(calculation)-457(is)-457(that,)]TJ -1 -1.122 Td [(because)-478(of)-478(the)-478(sparsene)20(ss)-478(of)-478(the)-478(obser)-60(vations)-478(over)-478(time,)-478(we)]TJ T* [(assumed)-249(that)-249(any)-249(discrepancie)20(s)-249(bet)-30(ween)-249(the)-249(model)-249(and)-249(the)-249(dat)-30(a)]TJ T* [(were)-190(due)-190(to)-190(independent)-190(rec)-30(ording)-190(errors.)-190(Because)-190(modeling)-190(the)]TJ 0.0076 Tc T* [(\(positive\))-631(autoc)-30(orrelation)-631(proce)20(ss)-631(probably)-631(would)-631(have)-631(in-)]TJ 0.005 Tc T* [(creased)-397(overall)-397(uncert)-30(aint)-30(y,)-397(this)-397(is)-397(a)-397(c)-30(onser)-60(vative)-397(assumption.)]TJ 0 -1.121 TD [(We)-244(thus)-244(assumed)-244(that)-244(stochasticit)-30(y)-244(in)-244(transmission)-244(was)-244(man)-30(ife)20(st)]TJ 0 -1.121 TD [(bet)-30(ween)-217(epidemics,)-217(rather)-217(than)-217(w)-40(ithin)-217(epidemics.)-217(Prev)-40(ious)-217(work)]TJ T* [(\(22,)-186(24\))-186(in)-186(c)-30(ontrast)-186(has)-186(focused)-186(on)-186(stochasticit)-30(y)-186(w)-40(ithin)-186(epidemics,)]TJ T* [(particularly)-347(that)-347(due)-347(to)-347(small)-347(population)-347(size)20(s.)-347(The)-347(population)]TJ T* [(size)20(s)-487(in)-487(our)-487(dat)-30(a)-487(set,)-487(however,)-487(were)-487(large)-487(enough)-487(that)-487(such)]TJ 0 -1.121 TD [(stochasticit)-30(y)-196(was)-196(probably)-196(weak)-196(\(Table)-196(3;)-196(ref.)-196(25\).)-196(A)-196(related)-196(issue)]TJ T* [(is)-317(that)-317(prev)-40(ious)-317(Baye)20(sian)-317(smallpox)-317(analyse)20(s)-317(have)-317(used)-317(the)-317(even)]TJ T* [(simpler)-363(SIR)-363(model)-363(and)-363(have)-363(c)-30(onsidered)-363(only)-363(single)-363(epidemics)]TJ T* [(\(26,)-201(27\))-201(or)-201(ex)-30(ponential)-201(g)-20(row)-30(th)-201(of)-201(the)-201(infected)-201(class)-201(\(17\).)-201(By)-201(using)]TJ T* [(the)-437(SEIR)-437(model,)-437(and)-437(by)-437(c)-30(onsidering)-437(multiple)-437(epidemics,)-437(our)]TJ T* [(e)20(stimate)20(s)-338(should)-338(better)-338(ref)-90(lect)-338(overall)-338(uncert)-30(aint)-30(y.)]TJ 1 -1.121 Td [(The)-610(likelihood)-610(was)-610(evaluated)-610(numerically)-610(by)-610(solv)-40(ing)-610(the)]TJ -1 -1.121 Td [(dif)-30(ferential)-447(equations)-447(w)-40(ith)-447(st)-30(andard)-447(methods)-447(\(see)-447(supporting)]TJ T* [(infor)-30(mation\).)-356(Because)-356(of)-356(the)-356(c)-30(omplex)-50(it)-30(y)-356(of)-356(the)-356(likelihood,)-356(the)]TJ T* [(posterior)-298(distribution)-298(can)-298(be)-298(for)-30(mulated)-298(only)-298(up)-298(to)-298(the)-298(propor-)]TJ T* [(tionalit)-30(y)-556(c)-30(onst)-30(ant)-556(and)-556(can)-556(be)-556(evaluated)-556(only)-556(point)-30(w)-40(ise.)-556(To)]TJ T* [(generate)-531(sample)20(s)-531(f)-30(rom)-531(the)-531(posterior,)-531(we)-531(therefore)-531(followed)]TJ T* [(st)-30(andard)-389(practice)-389(in)-389(using)-389(a)-389(Mark)-30(ov)-389(chain)-389(Monte)-389(Carlo)-389(algo-)]TJ T* [(rithm)-314(that)-314(replace)20(s)-314(each)-314(multidimensional)-314(random)-314(draw)-314(w)-40(ith)-314(a)]TJ T* [(sequence)-515(of)-515(single-parameter,)-515(or)-515(at)-515(least)-515(lower-dimensional,)]TJ T* [(draws)-253(\(26\).)-253(We)-253(asse)20(ssed)-253(c)-30(onvergence)-253(by)-253(using)-253(st)-30(andard)-253(Brooks-)]TJ T* 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3.202 0 Td [(414:748)-90(\226751.)]TJ -15.264 -1.214 Td [(4.)-424(Bozzette)-281(SA,)-281(Boer)-281(R,)-281(Bhatnagar)-281(V,)-281(Brower)-281(JL,)-281(Keeler)-281(EB,)-281(Morton)-281(SC,)-281(Stoto)]TJ 1.183 -1.214 Td [(M)-30(A)-338(\(2003\))]TJ /T1_0 1 Tf 5.226 0 Td [(N)-338(Engl)-338(J)-338(Med)]TJ /T1_4 1 Tf 6.257 0 Td [(348:416)-90(\226)-90(425.)]TJ -12.666 -1.214 Td [(5.)-424(Halloran)-334(ME,)-334(L)-30(ongin)-30(i)-334(IM,)-334(Nizam)-334(A,)-334(Yang)-334(Y)-334(\(2002\))]TJ /T1_0 1 Tf 24.69 0 Td (Science)Tj /T1_4 1 Tf 3.467 0 Td [(298:1428)-90(\2261432.)]TJ -28.157 -1.214 Td [(6.)-424(Eubank)-351(S,)-351(Guclu)-351(H,)-351(Kumar)-351(VSA,)-351(Marathe)-351(MV,)-351(Srin)-30(ivasan)-351(A,)-351(Toroczk)-30(ai)-351(Z,)]TJ 1.183 -1.214 Td [(Wang)-338(N)-338(\(2004\))]TJ /T1_0 1 Tf 7.116 0 Td (Nature)Tj /T1_4 1 Tf 3.202 0 Td [(429:180)-90(\226184.)]TJ -11.501 -1.214 Td [(7.)-424(Riley)-196(S,)-196(Fraser)-196(C,)-196(Donnelly)-196(CA,)-196(Ghan)-30(i)-196(AC,)-196(Abu-Raddad)-196(LJ,)-196(Hedley)-196(AJ,)-196(Leung)]TJ 1.183 -1.214 Td [(GM,)-338(Ho)-338(LM,)-338(L)-30(am)-338(T)-60(H,)-338(Thach)-338(TQ,)]TJ /T1_0 1 Tf 15.857 0 Td [(et)-338(al)-30(.)]TJ /T1_4 1 Tf 2.451 0 Td (\(2003\))Tj /T1_0 1 Tf 3.133 0 Td (Science)Tj /T1_4 1 Tf 3.471 0 Td (300:1961\2261966.)Tj -26.096 -1.214 Td [(8.)-424(Keeling)-259(MJ,)-259(Woolhouse)-259(MEJ,)-259(May)-259(RM,)-259(Dav)-40(ie)20(s)-259(G,)-259(Grenfell)-259(BT)-259(\(2003\))]TJ /T1_0 1 Tf 31.977 0 Td (Nature)Tj /T1_4 1 Tf -30.794 -1.214 Td [(421:136)-90(\226142.)]TJ -1.183 -1.214 Td [(9.)-424(Mills)-338(CE,)-338(Robins)-338(JM,)-338(Lipsitch)-338(M)-338(\(2004\))]TJ /T1_0 1 Tf 19.335 0 Td (Nature)Tj /T1_4 1 Tf 3.202 0 Td [(432:904)-90(\226906.)]TJ -23.042 -1.214 Td [(10.)-424(Rohan)-30(i)-338(P,)-338(Keeling)-338(MJ,)-338(Grenfell)-338(BT)-338(\(2002\))]TJ /T1_0 1 Tf 20.932 0 Td [(Am)-338(Nat)]TJ /T1_4 1 Tf 3.741 0 Td [(159:469)-90(\226)-90(481.)]TJ -0.0146 Tc -24.673 -1.214 Td [(1)-19(1)-19(.)-443(Kaplan)-243(EH,)-243(Craf)-30(t)-243(DL,)-243(Wein)-243(LM)-243(\(2002\))]TJ /T1_0 1 Tf 18.448 0 Td [(P)-30(roc)-243(Natl)-243(Acad)-243(Sci)-243(USA)]TJ /T1_4 1 Tf 10.068 0 Td (99:10935\22610940.)Tj 0.0049 Tc -28.516 -1.214 Td [(12.)-424(Centers)-460(of)-460(Disease)-460(Control)-460(\(2002\))]TJ /T1_0 1 Tf 17.758 0 Td [(Smallpox)-460(Response)-460(Plan)-460(and)-460(Guidelines)]TJ /T1_4 1 Tf -16.07 -1.214 Td [(\(Centers)-338(Dis)-338(Control,)-338(Atlant)-30(a\),)-338(Techn)-30(ical)-338(Report)-338(Draf)-30(t)-338(3.0.)]TJ -1.688 -1.214 Td [(13.)-424(Un)-30(ited)-406(K)-30(ingdom)-406(Department)-406(of)-406(Health)-406(\(2003\))]TJ /T1_0 1 Tf 23.168 0 Td [(Guidelines)-406(for)-406(Smallpox)-406(Re-)]TJ -21.479 -1.214 Td [(sponse)-494(and)-494(Management)-494(in)-494(the)-494(Post-Eradication)-494(Era)]TJ /T1_4 1 Tf 23.883 0 Td [(\(U.K.)-494(Depart)-494(Health,)]TJ -23.883 -1.214 Td [(L)-30(ondon\),)-338(Techn)-30(ical)-338(Report)-338(Version)-338(2.)]TJ 35.812 25.5 Td [(14.)-424(Fenner)-246(F,)-246(Henderson)-246(DA,)-246(Arit)-30(a)-246(I,)-246(Jezek)-246(Z,)-246(L)-30(adnyi)-246(ID)-246(\(1998\))]TJ /T1_0 1 Tf 28.355 0 Td [(Smallpox)-246(and)-246(Its)]TJ -26.667 -1.214 Td (Eradication)Tj /T1_4 1 Tf 5.26 0 Td [(\(WHO,)-338(Geneva\).)]TJ -6.949 -1.214 Td [(15.)-424(Fenn)-217(EA)-217(\(2001\))]TJ /T1_0 1 Tf 8.842 0 Td [(Pox)-217(Amer)-30(icana:)-217(The)-217(Great)-217(Smallpox)-217(Epidemic)-217(of)-217(1775\226)-90(82)]TJ /T1_4 1 Tf 24.459 0 Td (\(Hill)Tj -31.612 -1.214 Td [(and)-338(Wang,)-338(New)-338(York\).)]TJ -1.688 -1.214 Td [(16.)-424(Wearing)-338(HJ,)-338(Rohan)-30(i)-338(P,)-338(Keeling)-338(MJ)-338(\(2005\))]TJ /T1_0 1 Tf 20.909 0 Td [(PLoS)-338(Med)]TJ /T1_4 1 Tf 4.883 0 Td [(2:621\226)-90(627.)]TJ -25.791 -1.214 Td 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[(\(WHO,)-338(Geneva\),)-338(Techn)-30(ical)-338(Report)-338(SE)]TJ /T1_1 1 Tf 0 Tc 17.172 0 Td (\002)Tj /T1_4 1 Tf 0.0049 Tc 0.505 0 Td (73.57.)Tj -28.869 -1.214 Td [(20.)-424(Gelfand)-338(HM,)-338(Posch)-338(J)-338(\(1971\))]TJ /T1_0 1 Tf 14.715 0 Td [(Am)-338(J)-338(Epidemiol)]TJ /T1_4 1 Tf 7.227 0 Td [(93:234)-90(\226237.)]TJ -21.942 -1.214 Td [(21.)-424(Mack)-338(TM)-338(\(1972\))]TJ /T1_0 1 Tf 9.53 0 Td [(J)-338(Infect)-338(Dis)]TJ /T1_4 1 Tf 5.186 0 Td (125:161\226169.)Tj -14.716 -1.214 Td [(22.)-424(Eichner)-338(M,)-338(Dietz)-338(K)-338(\(2003\))]TJ /T1_0 1 Tf 13.902 0 Td [(Am)-338(J)-338(Epidemiol)]TJ /T1_4 1 Tf 7.227 0 Td [(158:110)-90(\226117.)]TJ -21.13 -1.214 Td [(23.)-424(Rigau-Pe)]TJ 0.0046 Tc 5.227 0 Td [(\264rez)-338(JG)-338(\(1982\))]TJ /T1_0 1 Tf 0.0049 Tc 6.896 0 Td [(J)-338(Hist)-338(Med)]TJ /T1_4 1 Tf 4.955 0 Td [(37:423\226)-90(438.)]TJ -17.078 -1.214 Td [(24.)-424(O\222Neill)-338(PD,)-338(Becker)-338(NG)-338(\(2001\))]TJ /T1_0 1 Tf 15.654 0 Td (Biostatistics)Tj /T1_4 1 Tf 5.265 0 Td [(2:99)-90(\226108.)]TJ -20.919 -1.214 Td [(25.)-424(Daley)-203(DJ,)-203(Gan)-30(i)-203(J)-203(\(1999\))]TJ /T1_0 1 Tf 12.163 0 Td [(Epidemic)-203(Modelling:)-203(An)-203(Introduction)]TJ /T1_4 1 Tf 15.665 0 Td [(\(Cambridge)-203(Un)-30(iv)]TJ -26.14 -1.214 Td [(Pre)20(ss,)-338(Cambridge,)-338(UK\).)]TJ -1.688 -1.214 Td [(26.)-424(O\222Neill)-338(PD,)-338(Roberts)-338(GO)-338(\(1999\))]TJ /T1_0 1 Tf 16.117 0 Td [(J)-338(Roy)-338(Stat)-338(Soc)-338(A)]TJ /T1_4 1 Tf 7.543 0 Td (162:121\226129.)Tj -23.659 -1.214 Td [(27.)-424(Fearnhead)-338(P,)-338(Meligk)-30(otsidou)-338(L)-338(\(2004\))]TJ /T1_0 1 Tf 18.602 0 Td [(J)-338(Roy)-338(Stat)-338(Soc)-338(B)]TJ /T1_4 1 Tf 7.506 0 Td (66:771\226789.)Tj -26.108 -1.214 Td [(28.)-424(Brooks)-338(SP,)-338(Gelman)-338(A)-338(\(1998\))]TJ /T1_0 1 Tf 14.916 0 Td [(J)-338(Comput)-338(Graph)-338(Stat)]TJ /T1_4 1 Tf 9.486 0 Td [(7:434)-90(\226)-90(455.)]TJ -24.402 -1.214 Td [(29.)-424(Geweke)-269(J)-269(\(1992\))-269(in)]TJ /T1_0 1 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