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1 BMJ Opn Forcasting and Control Policy Assssmnt for th Ebola Virus Disas (EVD) Epidmic in Sirra Lon Using Small- World Ntworkd Modl Simulations Journal: BMJ Opn Manuscript ID: bmjopn-0-00 Articl Typ: Rsarch Dat Submittd by th Author: 0-May-0 Complt List of Authors: Sittos, Constantinos; National Tchnical Univrsity of Athns, Applid Mathmatics and Physical Scincs Anastassopoulou, Clo; Univrsity of Patras, Biology Russo, Lucia; Consiglio Nazional di Ricrca, Grigoras, Christos; Brown Univrsity, Mdical School <b>primary Subjct Hading</b>: Scondary Subjct Hading: Kywords: Epidmiology Halth policy, Infctious disass, Rsarch mthods, Global halth, Public halth EPIDEMIOLOGY, Public halth < INFECTIOUS DISEASES, INFECTIOUS DISEASES, PUBLIC HEALTH

2 Pag of BMJ Opn Titl Pag Forcasting and Control Policy Assssmnt for th Ebola Virus Disas (EVD) Epidmic in Sirra Lon Using Small-World Ntworkd Modl Simulations Constantinos I. Sittos, Clo Anastassopoulou, Lucia Russo, Christos Grigoras,, Elfthrios Mylonakis Authors affiliations: School of Applid Mathmatics and Physical Scincs, National Tchnical Univrsity of Athns, Athns, Grc. Division of Gntics, Cll and Dvlopmntal Biology, Dpartmnt of Biology, Univrsity of Patras, Patras, Grc. Consiglio Nazional di Ricrca, Napoli, Italy. Division of Infctious Disass, Rhod Island Hospital, Warrn Alprt Mdical School of Brown Univrsity, Providnc, RI, USA. Corrsponding author: Constantinos I. Sittos: Associat Profssor Computational Scinc & Enginring, School of Applid Mathmatics and Physical Scincs, National Tchnical Univrsity of Athns,, Hroon Polytchniou Str., GR- 0 Athns, Grc. Tl.: ; ksit@mail.ntua.gr Elfthrios Mylonakis, M.D., Ph.D., FIDSA, Dan's Profssor of Mdical Scinc (Mdicin, and Molcular Microbiology and Immunology), Chif, Infctious Disass Division, Warrn Alprt Mdical School of Brown Univrsity, Rhod Island Hospital Eddy Strt, POB, rd Floor, Suit /0, Providnc, RI 00, Tl: 0-- / Fax: 0--. Manuscript information: Numbr of Figurs/Tabls: / Word Count of Abstract: Word Count of Main-Body Txt: Word Count of Figur and Tabl Lgnds:

3 BMJ Opn Pag of Abstract Objctivs: As th Ebola Virus Disas (EVD) still ravags Sirra Lon, w aimd at analyzing th pidmic for th latst priod (Dcmbr, 0 -April, 0) using a small-world ntworkd modl and forcast its volution. Diffrnt policy-control scnarios that could lad to th containmnt of th pidmic wr also xamind. Mthods: W dvlopd a stochastic modl with.0 million individuals (th population of Sirra Lon) intracting through a small-world social ntwork with adjustabl dnsity. Th modl incorporats th main pidmiologic factors, including th ffct of burial practics to virus transmission. Th ffctiv rproductiv numbr (R) was also valuatd dirctly from th individual-basd simulations. Estimats of th pidmiologic variabls wr computd on th basis of th tim sris of th official cass as rportd by th Cntrs for Disas Control and Prvntion (CDC). Rsults: From Dcmbr, 0 to Fbruary, 0 th pidmic was in rcssion compard to prvious months, as indicatd by th stimatd ffctiv rproductiv numbr (R) of ~0. (% CI: 0.-0.). From Fbruary to April, 0 R ros abov criticality (~., % CI:.-.0), flashing a not of caution for th situation. Projcting until mid Jun, w prdictd that th pidmic will continu through July. Assssmnt of diffrnt policy-control scnarios showd that th currnt dnsity of th social ntwork should b rducd by mor than 0% to obtain R< and contain th pidmic soon. Conclusions: Our rsults call for an immdiat implmntation of drastic control masurs to contain th pidmic in Sirra Lon. Kywords: EBOV, Sirra Lon, Effctiv rproductiv numbr, Forcasting, Communicabl Disas Control

4 Pag of BMJ Opn Articl summary Strngths and limitations of this study - Th worst Ebola Virus Disas (EVD) pidmic in history continus to ravag Wst Africa. - Th mounting concrn rgarding th continuation of th Ebola Virus Disas (EVD) pidmic in Sirra Lon promptd us to invstigat th most rcnt transmission dynamics of th pidmic in th country. - Whil th numbr of nw cass in Sirra Lon sms to dclin and schools hav ropnd for th first tim in months, w flash a not of caution for th situation. - Our analysis rvals that unlss drastic control masurs ar takn immdiatly, th pidmic is not xpctd to fad out, but it will continu through July. - Th validity of th analysis dpnds on th accuracy of th publicly availabl data. As it has bn rportd thr might b a potntial undrrporting of th stimatd cass and daths. Howvr vn so, th outcom th analysis calls for immdiat action.

5 BMJ Opn Pag of Introduction Th worst Ebola Virus Disas (EVD) pidmic in history continus to ravag Wst Africa. Th pidmic bgan with th rport of cass and daths in Guina on March, 0 (). Libria rportd its first laboratory-confirmd cass on March 0, 0, whil th first cass in Sirra Lon wr rportd on May, 0 (). Following rgular daily population movmnts for trad and family visitation, th virus crossd th local porous intrnational bordrs, stablishing chains of transmission not just in small villags, whr it would hav bn asir to contain it, but also in larg urban cntrs. Insufficint public halth infrastructur, poor sanitation conditions, lack of ducation about th disas and unsaf traditional burial practics hav also contributd to th sprad of th pidmic in th rgion (). In Libria, on of th most affctd countris, as of April 0, 0, a total of 0,0 cass hav bn rcordd, whil th toll of dath has xcdd,0 (). In arly March a halt of th pidmic was announcd, and vn though a nw cas was confirmd on March 0, 0, th pidmic is considrd to hav casd, whil th situation in Sirra Lon is notably diffrnt. With mor than,0 cass and,00 daths until now, Sirra Lon xprincd a drop in nw cass in January 0 and authoritis loosnd mobilization rstriction masurs to support conomic activity (). Howvr, rcnt WHO updats on th status of th EVD pidmic in this Wst African nation rport a flar up (), with a significant incras among th community of fishrmn living in th coastal ara of Abrdn in Frtown (). Th synchronous occurrnc of ovr 0 cass suggstd thy had bn infctd by a singl sourc, possibly an unsaf burial (). In light of ths rcnt dvlopmnts, w analyzd th EVD pidmic dynamics in Sirra Lon for th priod btwn Dcmbr, 0 and April, 0, using an agntbasd, social ntwork modl that w rportd rcntly and that provd to provid accurat

6 Pag of BMJ Opn prdictions for th cas of Libria (). For this purpos, th latst official cas counts from WHO wr fittd to th modl, following th so-calld Equation-Fr approach (). Th stimation of ky pidmiologic paramtrs, such as th cas fatality rat, th pr-contact transmission probability and th man tim from symptoms onst to rcovry or to dath, allowd us to study th volving dynamics through th social transmission ntwork whos structur and dnsity ar also xamind. Through agnt-basd simulations, w found that th indicativ of scondary infctions, ffctiv rproductiv numbr (R) was raisd abov criticality (~., % CI:.-.0) from Fbruary to April. W thus xplord diffrnt policy-control scnarios that could lad to rducd R valus, and, thrby, to th containmnt of th pidmic. Mthods W dvlopd an individual-basd modl for th study of th Ebola pidmic () with N individuals that intract through a Watts & Strogatz (WS) () small-world ntwork that approximats som attributs of th ral social intractions, which ar charactrizd by rlativly high clustring and short social distancs btwn thm. Hr, th ntwork was constructd with th Nwman-Watts () algorithm, in which short-cut dgs ar addd btwn pairs of nods with a probability, in th sam way as in a WS ntwork, but without rmoving dgs from th undrlying lattic. Th algorithm starts with a on-dimnsional ring ntwork with k local-narst nighbors pr nod and with a probability addd btwn two nods. Hnc, th man numbr of additional shortcuts is th man total dgr of th ntwork is k N (+ p rw that a link is p rw p rw ). In th constructd small-world k N, and ntwork w can adjust th dnsity of th ntwork, say α, at will, by randomly adding or subtracting th rquird numbr of links.

7 BMJ Opn Pag of Agnts ar catgorizd in fiv discrt stats: Suscptibl ( S ), Exposd ( E ), Infctd ( I ), Dad of th disas but not yt burid ( D ) I, and Dad of th disas and safly burid ( D b). Th D I infctious stat includs agnts who di, but whos burial ntails risk for onward virus transmission. Th transition btwn stats is modld as a discrt-tim, discrt stat non-markov random procss. Within this framwork, th stat spac ovr th st of th ntwork links is rprsntd by Y ( V), whr Y( v ) Y { S, E, I, D, D, R} th st of th stats of individual v k. = is k vk b I Th agnt-basd ruls that govrn th dynamics of th pidmic on a daily basis rad as follows: ( v ( ) b v ( ) I) p Y t+ = D Y t = D = () k k ( ( ) ( ), ( ) ) p Y t+ = E Y t = I Y t = D = p, vk vl vl I s E ( ( ) ( ) ) vk vk E I vl R v k () p Y t+ = I Y t = E = p () ( ( ) ( ) ) p Y t+ = D Y t = I = p () vk I vk I D ( ( ) ( ) ) p Y t+ = R Y t = I = p () vk vk I R whr ps E is th pr infctd contact transmission probability (still aliv or dad, but not yt burid), pe I, is th invrs of th incubation priod, pi D is th invrs of th tim from symptoms onst to dath, pi R is th invrs of th rcovry priod, and, p D/ I, is th ratio of daths to th infctd population. Th rat of th incubation priod is takn to b constant, st at pe I =, as rportd by th Who Ebola Rspons Tam (0). Rv k dnots th nighborhood of an individual v k. This first rul sts th tim priod from dath to burial to

8 Pag of BMJ Opn two days, during which family mmbrs and lovd ons may b infctd du to physical contact with th dad, still-contagious body. Long-rang links of a dad, yt potntially infctious, agnt ar cut, rflcting th fact that only rlativs and clos community mmbrs can b infctd during unsaf funral practics and rits. Th scond rul implis that a suscptibl agnt gts xposd to th disas with a rat dtrmind by th probability ps E pr infctd contact (still aliv or dad, but not yt burid). Th third rul implis that an xposd agnt bcoms infctious with a rat dtrmind by th probability p E I, whos invrs corrsponds to th incubation priod, i.. th tim from xposur to symptoms onst. Ruls () and () dfin th cas fatality rat, p / : an agnt dis of th disas with a rat dtrmind by th probability pi D (whos invrs is th tim from symptoms onst to dath) (Rul ()); altrnativly, an agnt could rcovr with a rat dtrmind by th probability pi R (Rul ()). Th ffctiv rproductiv ratio R, dfind as th avrag numbr of scondary infctions producd by a typical infctiv prson, is also computd dirctly from th agnt- basd simulations. D I Basd on th dmographics rportd by th Unitd Nations (UN), th population of Sirra Lon is million (). Tim sris of th official cas counts from th Cntrs for Disas Control and Prvntion (CDC) wr usd for modl fitting (). Cas data, which includd cumulativ incidnc and cumulativ daths by dat of rport for Sirra Lon rtrivd on March, 0 wr found on () and compild from WHO cas rports. Simulations wr prformd using Dcmbr, 0 as an initial dat and a tim horizon of 0 days with an qual sliding window tim intrval; th last dat was April, 0. Thus, fittd valus of th ntwork and modl paramtrs, as wll as stimats of th ffctiv rproductiv ratio, wr computd in squncs of succdd tim intrvals of wks corrsponding to priods (Dcmbr, 0 Fbruary, 0 and Fbruary,

9 BMJ Opn Pag of April, 0). Th initial conditions for th starting dat of Dcmbr, 0 wr calculatd on th basis of agnt-basd simulations from May, 0, i.. th dat on which th first cass wr officially rportd from WHO (), following th procdur dscribd in dtail lswhr (). In particular, w obtaind th following (xpctd) numbrs for Dcmbr, 0: E 0 = 0, I 0 = 0, D 0 = 0, D 0 =, R 0 =; th stimatd cumulativ numbr of cass thn was,. b Th xpctd (avragd) valus of th agnts stats Y( v ) Y = { S, E, I, D, D, R} wr computd ovr N = ntwork ralizations and r I k vk b I N s =00 simulations for ach on of th ntwork ralizations. Th modl paramtrs wr fittd to th rportd data using a trust- rgion-rflctiv approach for nonlinar minimization, implmntd for paramtr stimation () xploiting th Equation-Fr approach (,-). Matlab () was th simulation nvironmnt of choic, whil th modl was programmd in Fortran 0 and linkd to Matlab through mx fils. To forcast th volution of th Ebola virus pidmic in Sirra Lon, w usd th valus of th modl paramtrs as stimatd in th last priod; th rsulting paramtr valus wr thn fd to th simulator using as coars initial conditions th valus of {,,,,, } S E I D D R as computd on April, 0. W tstd th ffct of control policy b I scnarios by rducing th dnsity of th ntwork structur as stimatd in th scond priod. Sparsr ntwork dnsitis could rflct partial isolation of th population, rstriction of social mobilization combind with an xpandd public campaign for incrasd awarnss. Rsults and Discussion Th cumulativ numbrs of infctd and dad obtaind by th modl compard to th rportd cass in Sirra Lon ar shown in Figur. As shown, our framwork succds in

10 Pag of BMJ Opn approximating th actual data for total cass and daths (). For xampl, on Dcmbr, 0 th numbr of total cass, as rportd by th WHO, was,00 and th numbr of daths was,, whil our simulations rsultd in, cass and ~,00 daths. On Fbruary, 0, th total cass and daths wr,0 and,0, rspctivly, and our simulations rsultd in,0 total cass and, daths. Finally, on April, 0, th rportd total cass and daths wr, and,, rspctivly; our simulations rsultd in, total cass and, daths. Th pidmiologic paramtrs that wr obtaind through th optimization approach ar illustratd in Figur and a summary of th stimatd pidmic paramtrs for th priod undr study, togthr with thir % confidnc intrvals, is prsntd in Tabl. Panl (a) dpicts th volution of th stimatd ntwork charactristics, illustrat th modl paramtrs p D/ I, pi R, pi D, and s E p and a, whil panls (b-) rw p that fit bst to th rportd EVD pidmic dynamics in th country. Th volution of th stimatd ffctiv rproductiv numbr R in Sirra Lon is shown in panl (f). Mor spcifically, th contact ntwork of Sirra Lon xhibits a rathr random structur with a rwiring switching probability ( ~0. (% CI: ~0.-0.) that falls down to ~0. (% CI: ) during th study priod (Figur a). A slight incras is shown in th dnsity ratio of th ntwork as rprsntd by a, which was ~0. (% CI: ~0.-0.) during th first priod (Dcmbr, 0 Fbruary, 0) and ~0. (% CI: 0.-0.) during th scond priod of th study (Fbruary, 0 April, 0) (Figur a). Th diffrncs of th ntwork charactristics btwn th priods indicat a mor clustrd, yt dnsr contact ntwork during th scond priod that could partially rflct a rlaxation of awarnss in th first priod, whn th pidmic smd to dclin. Th cas fatality rat ( p D/ I ) that was stimatd to b ~% (% CI: -%) for th priod xtnding from lat Dcmbr 0 to Fbruary 0, incrasd to ~% (% CI: p rw ) of

11 BMJ Opn Pag 0 of %) from Fbruary to April (Figur b). Th xpctd priod from th onst of p symptoms to rcovry (i.., th invrs of I R ) was ~. days (% CI:.-0. days) during th first priod and ~ days (% CI:.-0. days)for th scond priod of study (Figur c). Th xpctd priod from th onst of symptoms to dath (i.., th invrs of pi D ) was constant at ~. days (% CI:.-.0 days) during th priod of study (Figur d). Rgarding th pidmic paramtrs, our stimats ar quit clos to th ons rportd by th WHO Ebola Rspons Tam and othr groups. For xampl, Ansumana t al. (0) rportd a % CFR at Hastings cntr, whil th National Institut of Communicabl disass (NICD) rports a CFR of % for Sirra Lon on April, 0 (); a man of.% CFR was rportd for Sirra Lon from th WHO Ebola rspons tam as of Sptmbr, 0 (0). Goms t al. () rportd an ~ day-priod from th onst of symptoms to rcovry, whil in a rcnt study by th WHO Ebola rspons tam () a priod of 0. days (with a SD of. days) was rportd from symptoms onst to hospital discharg for individuals of oldr than yars old. In th sam papr, a priod of ~ days (with qual SD) is rportd from symptoms onst to dath for th sam ag group. Th sam dlay priod from symptoms onst to dath was also rportd in Ansumana t al. (0). Th pr-contact transmission probability ps E valus wr stimatd at ~0.0 (% CI: ) in th first priod and ~0.0 (% CI: ) in th scond priod (Figur ). Finally, th ffctiv rproductiv numbr 0 R, as computd using th agnt- basd simulator, was ~0. (% CI: 0.-0.) from Dcmbr, 0 to Fbruary, 0, rising up to ~. (%.-.0) from Fbruary, 0 to April, 0 (Figur f). Simulations show that th xpctd cumulativ numbr of infctd cass may rach as high as,00 by mid of Jun, whil th cumulativ numbr of dad may rach,0, if no

12 Pag of BMJ Opn furthr action is undrtakn. Hnc, w dcidd to prform an assssmnt of th impact of potntial control stratgis. Basd on th rcntly announcd isolation policy (), w simulatd th influnc on th pidmic dynamics of sparsr, with rspct to th stimatd ntwork dnsity of th scond priod, ntwork dnsitis, by 0%, 0%, 0%, 0% and 0%. W tstd ths scnarios by rducing analogously th xpctd dnsity of th contact ntwork as stimatd during th scond priod and running th agnt-basd simulation from April until mid of Jun 0, kping all othr valus of th modl paramtrs fixd. Th rsults of th xploration of ths diffrnt scnarios ar summarizd in Tabl and portrayd graphically in Figur. Th no furthr action cas, with rspct to th stimatd currnt ntwork structur is also dpictd in Figur for comparison. By applying a 0% rduction in th ntwork dnsity (yilding an a of ~0.), th xpctd rproductiv numbr R was stimatd to b ~.. Accordingly, for a 0% rduction in th ntwork dnsity (yilding an a of ~0.), R was stimatd to b ~.. Rductions of 0%, 0% and 0% yilding ntwork dnsitis of ~0., ~0. and ~0. rspctivly, rsultd in R valus of ~., ~. and ~.0 corrspondingly (Tabl ). As is shown vn larg rductions in th dnsity of th ntwork will not lowr th R blow unity soon. In rality, th rduction in th ntwork dnsity could potntially rflct analogous rductions in social intractions furthr to th currnt rstrictions of community mobilization. Exampls would includ raising public awarnss and/or strngthning mdical car. Th country's National Ebola Rspons Cntr has alrady announcd a -day lockdown that will affct around. million popl (0). Nvrthlss, it is worth noticing that vn with a 0% rduction in th social ntwork dnsity, th pidmic shows no signs of fading out until th mid of Jun and w stimat that nw cass will continu to b rcordd. In conclusion, w found that th EVD pidmic in Sirra Lon was in rcssion in th priod btwn Dcmbr, 0 through mid of Fbruary, 0, as rflctd by th

13 BMJ Opn Pag of < valu of th rproductiv numbr for this priod. Howvr, during th last priod (i.., from Fbruary to April, 0), th pidmic has spikd and th rproductiv numbr was stimatd to b wll abov criticality, with th potntial to prsist at this lvl byond th nd of Jun and through July. Control masurs associatd with mobilization rstrictions wr also valuatd. Our findings, supportd by ral pidmiologic data and th projction of a spilling ovr of th pidmic to mid of Jun, indicat that th masurs implmntd so far ar inadquat. Takn in thir totality, ths findings indicat that th pidmic, vn with strict control isolation policis in ffct, will go on through July with a probability of fading out thraftr if policis ar implmntd and consistntly kpt in plac. Immdiat, mor intns fforts ar ndd bfor furthr complications mrg. Rducing th ffctiv dnsity of th drivd contact small-world-lik ntwork, through limitd social intractions, has th potntial to improv th currnt situation.

14 Pag of BMJ Opn Contributorship statmnt Constantinos Sittos, Lucia Russo and Christos Grigoras contributd to th dvlopmnt of th modl. Constantinos Sittos and Clo Anastassopoulou contributd to th data collction, intrprtation of th data and drafting th papr. Elfthrios Mylonakis contributd to th intrprtation of th data and substantially rvisd th papr. All authors approvd th final manuscript and accptd accountability for all aspcts of th work. Compting intrsts Thr ar no compting intrsts. Funding Statmnt This rsarch rcivd no spcific grant from any funding agncy in th public, commrcial or not-for-profit sctors. Data Sharing Statmnt Th data usd in this study ar publicly availabl from CDC at

15 BMJ Opn Pag of Rfrncs. Baiz S, Panntir D, Ostrich L, Rigr T, Koivogui L, Magassouba N, t al. Emrgnc of Zair Ebola virus disas in Guina. N Engl J Md. 0; :-. PubMd PMID:0. Ebola virus disas (EVD) in Wst Africa: an xtraordinary pidmic. Wkly Epidmiol Rc. 0;0:-. 0 Ebola Outbrak in Wst Africa. Cntrs for Disas Control and Prvntion. Accssd Mar 0. Koroma EB. Addrss to th Nation on th Ebola crisis. Jan 0. Accssd Mar 0. Tracking Ebola in th fishing community of Abrdn in Frtown, Sirra Lon. Mar 0. Accssd Mar 0. Sittos C, Anastassopoulou C, Russo L, Grigoras C, Mylonakis E. Modling th 0 Ebola Virus Epidmic Agnt-Basd Simulations, Tmporal Analysis and Futur Prdictions for Libria and Sirra Lon. PLOS Currnts Outbraks. 0 Mar. Edition. Kvrkidis IG, Gar CW, Hyman JM, Kvrkidis PG, Runborg O, Thodoropoulos C. Equation-fr, coars-graind multiscal computation: nabling microscopic simulators to prform systm-lvl analysis. Commun. Math. Sci. 00; :. Watts DJ, Strogatz SH. Collctiv dynamics of 'small-world' ntworks. Natur ;:0-. Nwman, MEJ, Watts DJ. Scaling and prcolation in th small-world ntwork modl. Physical Rviw E ; 0: Aylwar B, Barboza P, Bawo L, Pharm B, Brthrat E, Bilivogui P. t al.; Who Ebola Rpons Tam. Ebola virus disas in Wst Africa--th first months of th pidmic and forward projctions. N Engl J Md. 0; :-. /0.0/NEJMoa00. Sirra Lon. Unitd Nations Statistics Division. Accssd Mar Accssd Mar 0.. Colman TF, Li Y. An intrior trust rgion approach for nonlinar minimization subjct to bounds. SIAM J Optim. ; :-. /0./000. Makv AG, Maroudas D, Kvrkidis IG. Coars stability and bifurcation analysis using stochastic simulators: Kintic Mont Carlo xampls. J Chm Phys. 00; :00-.

16 Pag of BMJ Opn Gar CW, Kvrkidis IG, Thodoropoulos C. Coars intgration/bifurcation analysis via microscopic simulators: micro-galrkin mthods. Comput Chm Eng. 00; :-. /0.0/S00-(0) Thodoropoulos C, Qian YH, Kvrkidis IG. Coars stability and bifurcation analysis using tim-stpprs: a raction-diffusion xampl. Proc Natl Acad Sci U S A. 000;: /0.0/pnas...0. Sittos CI, Graham MD, Kvrkidis IG. Coars Brownian dynamics for nmatic liquid crystals: Bifurcation, projctiv intgration, and control via stochastic simulation. J Chm Phys. 00; :0-. Kvrkidis IG, Gar CW, Hummr G. Equation-fr: Th computr-aidd analysis of complx multiscal systms. AIChE J. 00; 0:-. /0.00/aic.00. MATLAB. Th MathWorks Inc Ansumana R, Jacobsn KH, Idris M, Bangura H, Boi-Jalloh M, Lamin JM. Et al. Ebola in Frtown ara, Sirra Lon a cas study of patints. N Engl J Md 0; :-. /0.0/NEJMc. Goms MFC, Pastor y Piontti A, Rossi L, Chao D, Longini I, Halloran ME, t al. Assssing th intrnational sprading risk associatd with th 0 Wst African Ebola outbrak. PLOS Currnts Outbraks. 0 Sp. Edition. /0./currnts.outbraks.cdfd0afddadf0da. Agua-Agum J, Ariyarajah A, Blak IM, Cori A, Donnlly CA, Dorigatti I, t al.;who Ebola Rpons Tam. Ebola Virus Disas among Childrn in Wst Africa. N Engl J Md 0; :-. /0.0/NEJMc. Ebola crisis: Sirra Lon lockdown to hit.m popl. BBC Nws. Mar 0. Accssd Mar 0.

17 BMJ Opn Pag of Tabl. Ky pidmiologic faturs of th Ebola Virus Disas (EVD) pidmic in Sirra Lon stimatd by th modl during th first and scond study priod (Dcmbr, 0 - April, 0). Sirra Lon Priod Variabl Man % CI First (Dc. - Fb., 0) Scond (Fb. -April., 0) rw p rw Ntwork dnsity (α) Tim to dath (Days)..-.0 Tim to rcovry (Days)..-0. CFR (%) - R p rw Ntwork dnsity (α) Tim to dath (Days)..-.0 Tim to rcovry (Days) CFR (%) -0 R..-.0 p, Rwiring switching probability; CFR, Cas fatality rat ( p D/ I ); R, Effctiv rproductiv numbr

18 Pag of BMJ Opn Tabl. Outcoms of isolation control policy scnarios on th basis of th xpctd rproductiv numbr R, as computd by running th agnt-basd simulation from April to th mid of Jun 0 (kping fixd all othr valus of th modl paramtrs). Sparsr dnsity rfrs to a prcnt rduction of th xpctd dnsity of th contact ntwork compard to th 0. valu that was stimatd for th scond priod (Fbruary April, 0). Priod % Sparsr dnsity Ntwork dnsity (α) R (April - Jun,, 0) 0% ~0. ~. 0% ~0. ~. 0% ~0. ~. 0% 0% ~0. ~0. ~. ~.0

19 BMJ Opn Pag of FIGURE LEGENDS Figur. Simulation Rsults for Sirra Lon from Dcmbr, 0 to April, 0. Expctd cumulativ cass of infctd (dottd rd) and dad (dottd black). WHO data ar dpictd by solid lins. Th priod undr study has bn tssllatd into two windows with a lngth of 0 days ach. For ach window, th modl paramtrs ar stimatd basd on th data rportd from WHO. Figur. Estimatd modl paramtrs for Sirra Lon from Dcmbr, 0 to April, 0. (a) Evolution of contact ntwork charactristics: switching probability ( p ) rw and dnsity ratio of th transmission ntwork ( a ). (b) Cas fatality rat ( p D/ I ). (c) /{rcovry priod} ( pi R ). (d) /{priod from inst of symptoms to dath} ( pi D ). () Pr- contact transmission probability ( ps E ). (f) Effctiv rproductiv numbr ( R ). % Confidnc intrvals ar also shown. Figur. Forcasting of th volution of th pidmic from April, to Jun, 0 undr diffrnt control scnarios. Ntwork dnsity valus wr compard to th dnsity of th social ntwork stimatd for th priod Fbruary -April, 0. (a) Total Cass, (b) Daths. Th no furthr action scnario is also dpictd.

20 Pag of BMJ Opn Figur. Simulation Rsults for Sirra Lon from Dcmbr, 0 to April, 0. Expctd cumulativ cass of infctd (dottd rd) and dad (dottd black). WHO data ar dpictd by solid lins. Th priod undr study has bn tssllatd into two windows with a lngth of 0 days ach. For ach window, th modl paramtrs ar stimatd basd on th data rportd from WHO.

21 BMJ Opn Pag 0 of Figur. Estimatd modl paramtrs for Sirra Lon from Dcmbr, 0 to April, 0. (a) Evolution of contact ntwork charactristics: switching probability and dnsity ratio of th transmission ntwork. (b) Cas fatality rat. (c) /{rcovry priod}. (d) /{priod from inst of symptoms to dath}. () Pr-contact transmission probability. (f) Effctiv rproductiv numbr. % Confidnc intrvals ar also shown. xmm (00 x 00 DPI)

22 Pag of BMJ Opn Figur. Forcasting of th volution of th pidmic from April, to Jun, 0 undr diffrnt control scnarios. Ntwork dnsity valus wr compard to th dnsity of th social ntwork stimatd for th priod Fbruary -April, 0. (a) Total Cass, (b) Daths. Th no furthr action scnario is also dpictd. xmm (00 x 00 DPI)

23 BMJ Opn Forcasting and Control Policy Assssmnt for th Ebola Virus Disas (EVD) Epidmic in Sirra Lon Using Small- World Ntworkd Modl Simulations Journal: BMJ Opn Manuscript ID bmjopn-0-00.r Articl Typ: Rsarch Dat Submittd by th Author: -Sp-0 Complt List of Authors: Sittos, Constantinos; National Tchnical Univrsity of Athns, Applid Mathmatics and Physical Scincs Anastassopoulou, Clo; Univrsity of Patras, Biology Russo, Lucia; Consiglio Nazional di Ricrca, Grigoras, Christos; Rhod Island Hospital, Providnc, Rhod Island; and Warrn Alprt Mdical School of Brown Univrsity, Providnc, Rhod Island, Infctious Disass Division Mylonakis, E; Rhod Island Hospital, Providnc, Rhod Island; and Warrn Alprt Mdical School of Brown Univrsity, Providnc, Rhod Island, Infctious Disass Division <b>primary Subjct Hading</b>: Scondary Subjct Hading: Kywords: Epidmiology Halth policy, Infctious disass, Rsarch mthods, Global halth, Public halth EPIDEMIOLOGY, Public halth < INFECTIOUS DISEASES, INFECTIOUS DISEASES, PUBLIC HEALTH

24 Pag of BMJ Opn Titl Pag Forcasting and Control Policy Assssmnt for th Ebola Virus Disas (EVD) Epidmic in Sirra Lon Using Small-World Ntworkd Modl Simulations Constantinos I. Sittos, Clo Anastassopoulou, Lucia Russo, Christos Grigoras,, Elfthrios Mylonakis Authors affiliations: School of Applid Mathmatics and Physical Scincs, National Tchnical Univrsity of Athns, Athns, Grc. Division of Gntics, Cll and Dvlopmntal Biology, Dpartmnt of Biology, Univrsity of Patras, Patras, Grc. Consiglio Nazional di Ricrca, Napoli, Italy. Division of Infctious Disass, Rhod Island Hospital, Warrn Alprt Mdical School of Brown Univrsity, Providnc, RI, USA. Corrsponding author: Constantinos I. Sittos: Associat Profssor Computational Scinc & Enginring, School of Applid Mathmatics and Physical Scincs, National Tchnical Univrsity of Athns,, Hroon Polytchniou Str., GR- 0 Athns, Grc. Tl.: ; ksit@mail.ntua.gr Elfthrios Mylonakis, M.D., Ph.D., FIDSA, Dan's Profssor of Mdical Scinc (Mdicin, and Molcular Microbiology and Immunology), Chif, Infctious Disass Division, Warrn Alprt Mdical School of Brown Univrsity, Rhod Island Hospital Eddy Strt, POB, rd Floor, Suit /0, Providnc, RI 00, Tl: 0-- / Fax: 0--. Manuscript information: Numbr of Figurs/Tabls: / Word Count of Abstract: Word Count of Main-Body Txt: Word Count of Figur and Tabl Lgnds:

25 BMJ Opn Pag of Abstract Objctivs: As th Ebola Virus Disas (EVD) is still sustaind in Sirra Lon, w analyzd th pidmic for th latst priod (Dcmbr, 0 -April, 0) using a small-world ntworkd modl and forcastd its volution. Policy-control scnarios for th containmnt of th pidmic wr also xamind. Mthods: W dvlopd an agnt-basd modl with million individuals (th population of Sirra Lon) intracting through a small-world social ntwork. Th modl incorporats th main pidmiologic factors, including th ffct of burial practics to virus transmission. Th ffctiv rproductiv numbr (R) was valuatd dirctly from th agnt-basd simulations. Estimats of th pidmiologic variabls wr computd on th basis of th official cass as rportd by th Cntrs for Disas Control and Prvntion (CDC). Rsults: From Dcmbr, 0 to Fbruary, 0 th pidmic was in rcssion compard to prvious months, as indicatd by th stimatd ffctiv rproductiv numbr (R) of ~0. (% CI: 0.-0.). From Fbruary to April, 0, R ros abov criticality (~., % CI:.-.), flashing a not of caution for th situation. By projcting in tim, w prdictd that th pidmic would continu through July 0. Our prdictions wr clos to th cass rportd by CDC by th nd of Jun, vrifying th criticality of th situation. In light of ths dvlopmnts, whil rvising our manuscript, w xpandd our analysis to includ th most rcnt data (until August, 0). By mid- August, R has falln blow criticality and th pidmic is xpctd to fad out by arly Dcmbr 0. Conclusions: Our rsults call for th continuation of drastic control masurs, which in th absnc of an ffctiv vaccin or thrapy at prsnt can only translat to isolation of th infctd sction of th population, to contain th pidmic. Kywords: EBOV, Sirra Lon, Effctiv rproductiv numbr, Forcasting, Communicabl Disas Control, Agnt-Basd Modling, Social Transmission Ntwork

26 Pag of BMJ Opn Articl summary Strngths and limitations of this study - Th gratst strngth of this study stms from th undrtakn mathmatical approach of choic, intgrating agnt-basd modling on complx ntworks and th so-calld Equation-Fr approach, which allowd us to assss various important pidmiologic paramtrs and to obtain accurat short-trm forcasts of th volution of th Ebola Virus Disas (EVD) pidmic in Sirra Lon. - Anothr advantag of th proposd mthodology is that it allows for th rapid valuation of diffrnt policy-control scnarios that could lad to th containmnt of th pidmic. - Our prdictions wr vrifid by th official cas count rportd by CDC. An updatd analysis considring data until mid August shows that th pidmic is xpctd to fad out by arly Dcmbr 0. - Th validity of a modling analysis dpnds on th accuracy of input data. Th most important limitation of our study prtains to th quality and accuracy of th outbrak data that wr fd to th mathmatical modl compard to th ral figurs. Undrrporting of cass and daths is crtainly to b xpctd undr th particular circumstancs of such a svr pidmic volving in on of th most impovrishd countris in th world. Howvr, vn so, th outcom th analysis calls for th continuation of control masurs to contain th pidmic.

27 BMJ Opn Pag of Introduction Th worst Ebola Virus Disas (EVD) pidmic in history continus to ravag Wst Africa. Th pidmic bgan with th rport of cass and daths in Guina on March, 0 (). Libria rportd its first laboratory-confirmd cass on March 0, 0, whil th first cass in Sirra Lon wr rportd on May, 0 (). Following rgular daily population movmnts for trad and family visitation, th virus crossd th local porous intrnational bordrs, stablishing chains of transmission not just in small villags, whr it would hav bn asir to contain it, but also in larg urban cntrs. Insufficint public halth infrastructur, poor sanitation conditions, lack of ducation about th disas and unsaf traditional burial practics hav also contributd to th sprad of th pidmic in th rgion (). In Libria, on of th most affctd countris, as of April 0, 0, a total of 0,0 cass hav bn rcordd, whil th toll of dath has xcdd,0 (). In arly March a halt of th pidmic was announcd, and vn though a nw cas was confirmd on March 0, 0, th pidmic is considrd to hav casd, whil th situation in Sirra Lon is notably diffrnt. With mor than,0 cass and,00 daths until now, Sirra Lon xprincd a drop in nw cass in January 0 and authoritis loosnd mobilization rstriction masurs to support conomic activity (). Howvr, rcnt World Halth Organization WHO updats on th status of th EVD pidmic in this Wst African nation rport a flar up (), with a significant incras among th community of fishrmn living in th coastal ara of Abrdn in Frtown (). Th synchronous occurrnc of ovr 0 cass suggstd thy had bn infctd by a singl sourc, possibly an unsaf burial (). In light of ths rcnt dvlopmnts, w analyzd th EVD pidmic dynamics in Sirra Lon for th priod btwn Dcmbr, 0 and April, 0, using an agnt- basd, social ntwork modl that w rportd rcntly and that provd to provid accurat prdictions for th cas of Libria (). For this purpos, th latst official cas counts from WHO wr fittd to th modl, following th so-calld Equation-Fr approach (). Our objctiv was to obtain stimats of ky pidmiologic paramtrs, such as th cas fatality rat, th pr-contact transmission probability and th man tim from symptoms onst to rcovry or to dath, in ordr to study th volving dynamics through th social transmission ntwork whos structur and dnsity ar also xamind. Through agnt-basd simulations, w found that th indicativ of scondary infctions, ffctiv rproductiv numbr (R) was raisd abov criticality (~., % CI:.-.0) from Fbruary to April, 0. W

28 Pag of BMJ Opn thus xplord diffrnt policy-control scnarios that could lad to rducd R valus, and, thrby, to th containmnt of th pidmic. Whil rvising our manuscript, w also procssd th rportd data from CDC of th vry last priod (April -August, 0), obtaining mor optimistic stimats indicativ of a rmission of th pidmic in Sirra Lon, as rflctd by th drivd R for th priod Jun -August, 0 (~0., % CI: 0.-.0). Projcting from August, w stimat that th pidmic will fad out in arly Dcmbr.

29 BMJ Opn Pag of Mthods W dvlopd an agnt-basd modl for th study of th Ebola pidmic () with N individuals that intract through a Watts & Strogatz (WS) () small-world ntwork that approximats som attributs of th ral social intractions, which ar charactrizd by rlativly high clustring and short social distancs btwn thm. Hr, th ntwork was constructd with th Nwman-Watts () algorithm, in which short-cut dgs ar addd btwn pairs of nods with a probability, in th sam way as in a WS ntwork, but without rmoving dgs from th undrlying lattic. Th algorithm starts with a on-dimnsional ring ntwork with k local-narst nighbors pr nod and with a probability p rw that a link is addd btwn two nods. Hnc, th man numbr of additional shortcuts is p th man total dgr of th ntwork is k N (+ p rw ). In th constructd small-world rw k N, and ntwork w can adjust th dnsity of th ntwork, say α, at will, by randomly adding or subtracting th rquird numbr of links. Agnts ar catgorizd in fiv discrt stats: Suscptibl ( S ), Exposd ( E ), Infctd ( I ), Dad of th disas but not yt burid ( D ) ( D ) b I, Dad of th disas and safly burid, and Rcovrd (R) (). Th D I infctious stat includs agnts who di, but whos burial ntails risk for onward virus transmission. Th transition btwn stats is modld as a discrt-tim, discrt stat non-markov random procss. Within this framwork, th stat spac ovr th st of th ntwork links is rprsntd by Y ( V), whr ( ) {,,,,, } Y v Y = S E I D D R is th st of th stats of individual v k. k vk b I Th agnt-basd ruls that govrn th dynamics of th pidmic on a daily basis rad as follows: ( v ( ) b v ( ) I) p Y t+ = D Y t = D = () k k ( ( ) (), () ) p Y t+ = E Y t = I Y t = D = p, vk vl vl I s E ( ( ) () ) vk vk E I vl R v k () p Y t+ = I Y t = E = p () ( ( ) () ) p Y t+ = D Y t = I = p () vk I vk I D ( ( ) () ) p Y t+ = R Y t = I = p () vk vk I R

30 Pag of BMJ Opn whr ps E is th pr infctd contact transmission probability (still aliv or dad, but not yt burid), pe I, is th invrs of th incubation priod, pi D is th invrs of th tim from symptoms onst to dath, pi R is th invrs of th rcovry priod, and, p D/ I, is th ratio of daths to th infctd population (). Th rat of th incubation priod is takn to b constant, st at pe I =, as rportd by th Who Ebola Rspons Tam (0). Rv k dnots th nighborhood of an individual v k. This first rul sts th tim priod from dath to burial to two days, during which family mmbrs and lovd ons may b infctd du to physical contact with th dad, still-contagious body. Long-rang links of a dad, yt potntially infctious, agnt ar cut, rflcting th fact that only rlativs and clos community mmbrs can b infctd during unsaf funral practics and rits. Th scond rul implis that a suscptibl agnt gts xposd to th disas with a rat dtrmind by th probability ps E pr infctd contact (still aliv or dad, but not yt burid). Th third rul implis that an xposd agnt bcoms infctious with a rat dtrmind by th probability p E I, whos invrs corrsponds to th incubation priod, i.. th tim from xposur to symptoms onst. Ruls () and () dfin th cas fatality rat, p D/ I : an agnt dis of th disas with a rat dtrmind by th probability pi D (whos invrs is th tim from symptoms onst to dath) (Rul ()); altrnativly, an agnt could rcovr with a rat dtrmind by th probability pi R (Rul ()). Th ffctiv rproductiv ratio R, dfind as th avrag numbr of scondary infctions producd by a typical infctiv prson, is also computd dirctly from th agnt- basd simulations. Basd on th dmographics rportd by th Unitd Nations (UN), th population of Sirra Lon is million (). Tim sris of th official Ebola cas counts from th Cntrs for Disas Control and Prvntion (CDC) wr usd for modl fitting (). Ths cas counts wr collctd from public data rlasd by th World Halth Organization (WHO) () and CDC (). Evn though ths data sts do not distinguish btwn suspct, probabl and laboratory-confirmd cas counts, thy ar considrd to rprsnt th bst availabl stimats of th currnt stat of th pidmic in th svrly afflictd Wst African countris. Cas data, which includd cumulativ incidnc and cumulativ daths by dat of rport for Sirra Lon, wr rtrivd on April, 0.

31 BMJ Opn Pag of Simulations wr prformd using Dcmbr, 0 as an initial dat and a tim horizon of 0 days with an qual sliding window tim intrval; th last dat was April, 0. Thus, fittd valus of th ntwork and modl paramtrs, as wll as stimats of th ffctiv rproductiv ratio, wr computd in squncs of succdd tim intrvals of 0 days corrsponding to priods (Dcmbr, 0 Fbruary, 0 and Fbruary, 0 April, 0). Th initial conditions for th starting dat of Dcmbr, 0 wr calculatd on th basis of agnt-basd simulations from May, 0, i.. th dat on which th first cass wr officially rportd from WHO (), following th procdur dscribd in dtail lswhr (). In particular, w obtaind th following (xpctd) numbrs for Dcmbr, 0: E 0 = 0, I 0 = 0, D 0 = 0, D 0 =, R 0 =; th stimatd cumulativ numbr of cass thn was,. b Th xpctd (avragd) valus of th agnts stats Y( v ) Y = { S, E, I, D, D, R} wr computd ovr N = ntwork ralizations and r I k vk b I N s =00 simulations for ach on of th ntwork ralizations. Th modl paramtrs wr fittd to th rportd data using a trust- rgion-rflctiv approach for nonlinar minimization, implmntd for paramtr stimation () xploiting th Equation-Fr approach (,-). Matlab () was th simulation nvironmnt of choic, whil th modl was programmd in Fortran 0 and linkd to Matlab through mx fils. To forcast th volution of th Ebola virus pidmic in Sirra Lon, w usd th valus of th modl paramtrs as stimatd in th last priod; th rsulting paramtr valus wr thn fd to th simulator using as coars initial conditions th valus of {,,,,, } S E I D D R as computd on April, 0. W tstd th ffct of control policy b I scnarios by rducing th dnsity of th ntwork structur as stimatd in th scond priod. Sparsr ntwork dnsitis could rflct partial isolation of th population, rstriction of social mobilization combind with an xpandd public campaign for incrasd awarnss.

32 Pag of BMJ Opn Rsults and Discussion Th cumulativ numbrs of infctd and dad obtaind by th modl compard to th rportd cass in Sirra Lon ar shown in Figur. Our framwork succds in approximating th actual data for total cass and daths (). For xampl, on Dcmbr, 0 th numbr of total cass, as rportd by th WHO, was,00 and th numbr of daths was,, whil our simulations rsultd in, cass and ~,00 daths. On Fbruary, 0, th total cass and daths wr,0 and,0, rspctivly, and our simulations rsultd in,0 total cass and, daths. Finally, on April, 0, th rportd total cass and daths wr, and,, rspctivly; our simulations rsultd in, total cass and, daths. Th pidmiologic paramtrs that wr obtaind through th optimization approach ar illustratd in Figur and a summary of th stimatd pidmic paramtrs for th priod undr study, togthr with thir % confidnc intrvals, is prsntd in Tabl. Panl (a) dpicts th volution of th stimatd ntwork charactristics, illustrat th modl paramtrs ps E, D/ I p and a, whil panls (b-) rw p, pi R and pi D that fit bst to th rportd EVD pidmic dynamics in th country. Th volution of th stimatd ffctiv rproductiv numbr R in Sirra Lon is shown in panl (f). Mor spcifically, th contact ntwork of Sirra Lon xhibits a rathr random structur with a rwiring switching probability ( ~0. (% CI: ~0.-0.) that falls down to ~0. (% CI: ) during th study priod (Figur a). A slight incras is shown in th dnsity ratio of th ntwork as rprsntd by a, which was ~0. (% CI: ~0.-0.) during th first priod (Dcmbr, 0 Fbruary, 0) and ~0. (% CI: 0.-0.) during th scond priod of th study (Fbruary, 0 April, 0) (Figur a). Th diffrncs of th ntwork charactristics btwn th two priods indicat a mor clustrd, yt dnsr contact ntwork during th scond priod that could partially rflct a rlaxation of awarnss in th first priod, whn th pidmic smd to dclin. Th cas fatality rat ( p D/ I ) that was stimatd to b ~% (% CI: -%) for th priod xtnding from lat Dcmbr 0 to Fbruary 0, incrasd to ~% (% CI: -0%) from Fbruary to April (Figur ). Th xpctd priod from th onst of symptoms to rcovry (i.., th invrs of pi R ) was ~. days (% CI:.-0. days) during th first priod and ~ days (% CI:.-0. days) for th scond priod of study (Figur c). Th xpctd tim intrval from th onst of symptoms to dath (i.., th invrs p rw ) of

33 BMJ Opn Pag 0 of of pi D ) was constant at ~. days (% CI:.-.0 days) during th priod of study (Figur d). Rgarding th pidmic paramtrs, our stimats ar quit clos to th ons rportd by th WHO Ebola Rspons Tam and othr groups. For xampl, Ansumana t al. (0) rportd a % CFR at Hastings cntr, whil th National Institut of Communicabl disass (NICD) rports a CFR of % for Sirra Lon on April, 0 (); a man of.% CFR was rportd for Sirra Lon from th WHO Ebola rspons tam as of Sptmbr, 0 (0). Goms t al. () rportd an ~ day-priod from th onst of symptoms to rcovry, whil in a rcnt study by th WHO Ebola rspons tam () a priod of 0. days (with a SD of. days) was rportd from symptoms onst to hospital discharg for individuals of oldr than yars old. In th sam papr, a priod of ~ days (with qual SD) is rportd from symptoms onst to dath for th sam ag group. Th sam dlay priod from symptoms onst to dath was also rportd in Ansumana t al. (0). Th pr-contact transmission probability ps E valus wr stimatd at ~0.0 (% CI: ) in th first priod and ~0.0 (% CI: ) in th scond priod (Figur b). Finally, th ffctiv rproductiv numbr R, as computd using th agnt- basd simulator, was ~0. (% CI: 0.-0.) from Dcmbr, 0 to Fbruary, 0 0, rising up to ~. (%.-.) from Fbruary, 0 to April, 0 (Figur f). Simulations show that th xpctd cumulativ numbr of infctd cass may rach as high as,00 by Jun, whil th cumulativ numbr of dad may xcd,00, if no furthr action is undrtakn. Hnc, w dcidd to prform an assssmnt of th impact of potntial control stratgis. Basd on th rcntly announcd isolation policy (), w simulatd th influnc on th pidmic dynamics of sparsr, with rspct to th stimatd ntwork dnsity of th scond priod, ntwork dnsitis, by 0%, 0%, 0%, 0% and 0%. W tstd ths scnarios by rducing analogously th xpctd dnsity of th contact ntwork as stimatd during th scond priod and running th agnt-basd simulation from April until Jun, 0, kping all othr valus of th modl paramtrs fixd. Th rsults of th xploration of ths diffrnt scnarios ar summarizd in Tabl and portrayd graphically in Figur. Th no furthr action cas, with rspct to th stimatd currnt ntwork structur is also dpictd in Figur for comparison. By applying a 0% rduction in th ntwork dnsity (yilding an a of ~0.), th xpctd rproductiv numbr R was stimatd to b ~.. Accordingly, for a 0% rduction in th ntwork dnsity 0

34 Pag of BMJ Opn (yilding an a of ~0.), R was stimatd to b ~.. Rductions of 0%, 0% and 0% yilding ntwork dnsitis of ~0., ~0. and ~0. rspctivly, rsultd in R valus of ~., ~. and ~.0 corrspondingly (Tabl ). As shown, vn larg rductions in th dnsity of th ntwork will not lowr th R blow unity soon. A study by Khan t al. that obtaind robust stimats for th basic rproductiv ratio R 0 in both Libria and Sirra Lon showd that ffctiv isolation is rquird to bring th valu of R 0 to lss than, and hnc control th outbrak (). Khan t al. suggstd that th contact rat in isolation should b lss than on quartr of that for th infctd non-isolatd population, and that, th fraction of high-risk individuals should b brought to lss than 0% of th ovrall suscptibl population, to halt th pidmic (). In rality, th rduction in th ntwork dnsity could potntially rflct analogous rductions in social intractions furthr to th currnt rstrictions of community mobilization. Exampls would includ raising public awarnss and/or strngthning mdical car. Th country's National Ebola Rspons Cntr has alrady announcd a -day lockdown that will affct around. million popl (0). Nvrthlss, it is worth noticing that vn with a 0% rduction in th social ntwork dnsity, th pidmic shows no signs of fading out until Jun and w stimat that nw cass will continu to b rcordd. In conclusion, w found that th EVD pidmic in Sirra Lon was in rcssion in th priod btwn Dcmbr, 0 through mid-fbruary, 0, as rflctd by th < valu of th rproductiv numbr for this priod. Howvr, during th scond study priod (i.., from Fbruary to April, 0), th pidmic has spikd and th rproductiv numbr was stimatd to b wll abov criticality, with th potntial to prsist at this lvl byond th nd of Jun and through July. Control masurs associatd with mobilization rstrictions wr also valuatd. Our findings, supportd by ral pidmiologic data and th projction of a spilling ovr of th pidmic to mid-jun, indicat that th masurs implmntd so far ar inadquat. Takn in thir totality, ths findings indicat that th pidmic, vn with strict control isolation policis in ffct, will go on through July with a probability of fading out thraftr if policis ar implmntd and consistntly kpt in plac. Immdiat, mor intns fforts ar ndd bfor furthr complications mrg. Rducing th ffctiv dnsity of th drivd contact small-world-lik ntwork, through limitd social intractions, has th potntial to improv th currnt situation. Our rsults and prdictions wr vrifid from th official data rportd by CDC for th corrsponding priod of study. Hnc, our approach sms promising to forcast r-mrgnt outbraks in othr vulnrabl rgions of Africa, such as Eastrn and Cntral Africa, whr Ebola outbraks hav

35 BMJ Opn Pag of traditionally occurrd in th past. Estimations through clinical studis of important factors such as th contact transmission probability, mortality and rcovry rat, incubation priods as wll as dtaild ag-spcific data as th pidmic dvlops in spac and tim, would nhanc our ability to bttr modl, forcast and dsign fficint control policis. Howvr, th usfulnss of mathmatical modls should not b ovrstimatd. Dspit th significant tchnological progrss and concntratd walth, brakdowns and cuts in public halth infrastructurs worldwid ar (th) major rasons for boosting pidmics. Libria and Sirra Lon, th two countris that hav bn worst affctd from th Ebola pidmic had an almost non-xistnt halth car systm: as rportd Libria with a population of mor than million popl had just physicians and Sirra Lon with a population xciting million had just physicians (). Updat to th cas of Sirra Lon (priod April -August, 0) Sinc th rsults w obtaind by analyzing th rportd data until April, 0 showd that th pidmic was sustaind in Sirra Lon, w dcidd to invstigat furthr th currnt trnds of th pidmic dynamics. Thrfor, w xpandd our analysis by taking into account th rportd data for th country for th vry last priod (April -August, 0). Th rsults of this xpandd analysis indicat a dclining trnd in th transmission potntial of th virus, as shown in Tabl. Mor spcifically, ( p rw ) ros significantly in th priod April -Jun, 0 to ~0. (% CI: ~0.-0.) with a furthr slight incras in th vry last priod (Jun -August, 0) to ~0. (% CI: ). Τh dnsity ratio of th ntwork as rprsntd by a, did not show significant changs: in th priod April - Jun, 0 it was found to b ~0. (% CI: ~0.-0.) and ~0. (% CI: 0.-0.) during th priod Jun -August, 0. Th cas fatality rat ( p D/ I ) droppd to ~0% (% CI: -%) for both last priods. Th xpctd priod from th onst of symptoms to rcovry (i.., th invrs of pi R ) was ~0 days (% CI: -0 days) during th priod April -Jun, 0 and ~ days (% CI: - days) for th priod Jun August, 0. Th xpctd priod from th onst of symptoms to dath (i.., th invrs of pi D ) was almost constant at ~.0 days (% CI:.-. days) for both last priods. Th pr- contact transmission probability ps E valus wr stimatd at ~0.0 (% CI: ) in th priod April -Jun and ~0.0 (% CI: ) in th priod Jun August, 0. Finally, th R obtaind through th agnt-basd simulations droppd to ~.