Using Mobile Phone Data to Reduce Spread of Disease

While human mobility has important benefits for economic growth, it can generate negative externalities. This paper studies the effect of mobility on the spread of disease in a low-incidence setting when people do not internalize their risks to others. Using malaria as a case study and 15 billion mobile phone records across nine million SIM cards, this paper causally quantifies the relationship between travel and the spread of disease. The estimates indicate that an infected traveler contributes to 1.7 additional cases reported in the health facility at the traveler's destination. This paper develops a simulation-based policy tool that uses mobile phone data to inform strategic targeting of travelers based on their origins and destinations. The simulations suggest that targeting informed by mobile phone data could reduce the caseload by 50 percent more than current strategies that rely only on previous incidence.


Policy Research Working Paper 9198
While human mobility has important benefits for economic growth, it can generate negative externalities. This paper studies the effect of mobility on the spread of disease in a low-incidence setting when people do not internalize their risks to others. Using malaria as a case study and 15 billion mobile phone records across nine million SIM cards, this paper causally quantifies the relationship between travel and the spread of disease. The estimates indicate that an infected traveler contributes to 1.7 additional cases reported in the health facility at the traveler's destination. This paper develops a simulation-based policy tool that uses mobile phone data to inform strategic targeting of travelers based on their origins and destinations. The simulations suggest that targeting informed by mobile phone data could reduce the caseload by 50 percent more than current strategies that rely only on previous incidence. This paper is a product of the Development Impact Evaluation Group, Development Economics. It is part of a larger effort by the World Bank to provide open access to its research and make a contribution to development policy discussions around the world. Policy Research Working Papers are also posted on the Web at http://www.worldbank.org/prwp. The author may be contacted at smilusheva@worldbank.org.
Using Mobile Phone Data to Reduce Spread of Disease * Sveta Milusheva JEL Classication: rSID sISD tIVD sIVD yIS Keywords: relthD ig dtD epidemisD moilityD puli poliyD moile phones * s m grteful to endrew posterD tesse hpiroD nd hniel fjorkegren for their ontinE uous guidne on this projetF s would like to thnk itor elegnD qirij forkerD hvid qlikD worgn rrdyD erinn vegoviniD imily ysterD xik uktnonhiD frye teinergD endrew tem nd illim iolette for vlule feedkF s ppreite the omments from prtiipnts t the orld fnk efghi gonfereneD the xihg gonfereneD the opov gonfereneD the opultion relth ienes orkshopD the ee gonferene nd the frown miroeonomis lunh seminrF hnk you to the fill 8 welind qtes poundtion @grnt yIIIRUWIA nd the xsgrrh @grnt QP rh UQQVEPWA for (nnil supportF enonymous moile phone dt hve een mde ville y yrnge nd ontel within the frmework of the hRhEenegl hllengeF s thnk hilippe quinot nd kou hieyeD er nd the xtionl wlri gontrol rogrm for providing the dt on mlri inidene nd helpful feedkF 1 Introduction snresing domesti nd interntionl moility hs mgni(ed the devstting onseE quenes of infetious disesesX more thn IIDHHH deths from iolD RRHDHHHEIDQHHDHHH ses of ik infetions in IQ ountriesD nd most reentlyD more thn IPSDHRV infetions nd RDTIQ deths from gyshEIW 1 ross IIU ountries @ fogoh et lF PHITD ry PHPHD ry PHPHAF xegtive externlities from moility re lso relevnt for longEstnding diseses tht we re iming to eliminteF por exmpleD enezuelD the (rst ountry erti(ed y the orld relth yrgniztion @ryA for eliminting mlri in its most populted res in IWTID exE periened drmti resurgene of the disese in PHIT in prt due to migrnt workers in the mining region eoming sikD trveling homeD nd spreding the disese to their home villges nd ities @gsey PHITAF his pper uses se study of mlri in enegl to demonstrte how to hrness ig dt to uslly estimte the size of this externlity of movement nd pply the results towrds more e'etive poliy trgetingF he methods n e pplied more rodly to inform poliies relted to mitigting spred of infetious disesesF he eonomis literture identi(es mlri erdition s hving importnt impts on dult inome nd onsumption @flekley PHIHD gutler et lF PHIHD enktrmni PHIPAD rel estte welth @rong PHIIAD longer term helth inluding hroni disese nd disility @rong PHIQAD test sores nd edutionl ttinment @frofskyD enekweD nd ghse PHISD vus PHIHD enktrmni PHIPAF 2 xinetyEnine ountries hve een erti(ed y the ry s mlri freeY howeverD uEhrn efriD whih ounted for WQ7 of ll mlri deths in PHIVD hs only hd single suessful se of elimintion @World Malaria Report PHIWAF hile previous work hs studied mlri preventionGtretment in shortEterm settingsD fousing on the priing of mlri interventions @tessi gohen nd hups PHIHD tessi gohenD hupsD show how ggregted ig dt on individuls9 geolotion n inform more ostEe'etive trgeting strtegies to redue trnsmission generted y popultion moilityD whih would e omplementry omponent of mpign to suessfully eliminte mlriF he negtive externlity from trvel is generted when people re unwre of their risks to others euse they do not know tht they re disese vetorsF 3 et given the ene(ts of trvelD n informtion mpign is unlikely to use people to internlize the externlity nd hoose not to trvel to prevent infeting othersF wesuring the size of the externlity nd identifying those people tht ontriute the most n llow for trgeted poliies tht n help ddress this mrket filureF he min hllenge in estimting the size of the externlity from moility is tht while disese trnsmission my respond quikly to hnges in migrtion ptternsD existing survey dt tht reord these ptterns re often infrequent or do not hve overge ross ountryF 4 hereforeD the only strtegy ville to poliymkers to ddress this externlity is using inidene in the previous yer to identify where nd who to trgetF his pper is le to signi(ntly improve on this strtegy y utilizing new soure of dt to trk popultion 3 As will be described in more detail in the next section, the long incubation period for malaria allows people to travel without knowing they are infected. Additionally, those in high malaria settings typically develop immunity and do not experience malaria symptoms yet can infect mosquitoes when they travel to low malaria settings. 4 In Senegal, the main ocial source of data on population movement is census data that only includes long-term migration statistics every 10 years. There are other surveys that ask about commuting, such as the Household Mobility Survey of Dakar (EMTASUD), but it is only for one point in time, it is focused only on Dakar, and it was done in 2000 and in 2015). movement for lrge numer of people etween helth fility thment res t the dily levelF s leverge moile phone metdt for WFS million sw rds in enegl in PHIQ to extrt ptterns of movement etween di'erent res from the pproximte lotions of IS illion lls nd textsF por eh month nd helth fility reD s mesure the numer of inoming trvelers from other regions weighted y the inidene of mlri in these regions nd the length of time spent in the origin nd destintion to lulte 4expeted imported mlri sesF4 s study n re of enegl lose to elimintion to fous on reintrodution e'etsF s use pnel dt strtegy to estimte the impt of imported inidene on totl mlri inidene in this lowEmlri setting using liner dynmi pnelEdt model nd ontrolling for time (xed e'etsF sf infeted trvelers only led to mlri se eing deteted in the destintion rther thn the origin of the trvelerD ut do not generte ny externlity in the form of dditionl mlri sesD then stndrd model would predit for eh expeted imported se one more dditionl se reported in the destintionF snstedD s (nd tht one dditionl expeted imported se of mlri in low mlri re leds to IFU ses of mlri reportedD inditing n externlity of FU new sesF qiven tht migrtion hs numerous eonomi nd soil ene(tsD poliymkers fe trdeEo's etween eonomi growth nd improving puli helth in designing poliies to redue trvelElinked mlri sesF his pper provides useful frmework for strtegi trgeting of highErisk popultions in lowEinidene res to redue negtive externlities from trvel with miniml interferene to trvel ptternsF here re two tegories of trgeting onsideredX @IA trgeting highErisk trvelers entering low mlri re from high mlri re nd @PA trgeting ll trvelers in only spei( res of lowEmlri regions tht re likely to reeive mny highErisk trvelersF 5 ithin eh typeD s ompre strtegy tht inorportes dily informtion on origins nd destintions of trvelers from moile phone dt with strtegies tht only use informtion on inidene in the previous yer tht ould e implemented y the government in the sene of moile phone dtF he most ostEe'etive strtegy is to use moile phone dt nd omine the two types of trgetingF yn vergeD given the existing udget ville for this type of tivityD the ostE e'etive strtegy using moile phone dt performs over SH7 etter ompred to the next est strtegy tht only relies on inidene in the previous yerF wy empiril design ounts for onfounders orrelted with movementF sing rinfll proxies nd month (xed e'etsD s ontrol for sesons nd holidysD whih drive lrge mount of migrtion in eneglF s lso test tht it is not n unoservle orrelted with oth migrtion nd mlri driving the resultsD ut insted the omintion of movement nd the mlri levels t origins nd destintionsF edditionl heks show tht the reltionship etween imported inidene nd mlri inidene is not driven y some other reltionship etween origins nd destintions s well s to ensure tht the reltionship holds only for mlri nd not for other helth onditionsF s lso test the impt of future imported inidene on mlri inidene in the urrent month nd (nd no reltionshipF his pper uilds on previous helth literture tht hs estlished trvel s risk ftor for ontrting mlriD @wontlvo nd eynlEuerol PHHUD vynh et lF PHISD ysorioD oddD nd frdley PHHRD iri et lF PHIHD vittrell et lF PHIQAD y estimting the size of the usl impt from n expeted imported seD whih mkes it possile to ondut poliy simultions nd ompre di'erent trgeting strtegiesF tem et lF @PHHWA nd ve wenh et lF @PHIIA use three months of ell phone dt to estimte the mlri importtion rte to nzir using stti model tht does not ount for sesonlity due to the limited time frme of their moile phone dtF imilrlyD esolowskiD igleD et lF @PHIPAD inns nd emusi @PHIQAD ghng et lF @PHIVA nd shntmll et lF @PHIVA mong othersD do not inorporte sesonlity in inidene nd fous on identifying potentil soures nd sinks sed on trvel ptterns nd nnul mlri prevlene dtF et fukeeD temD nd tF wetlf @PHIUA point out tht sesonl vrition in iologil ftors relted to limte nd sesonl popultion movements re importnt for mny infetious diseses nd filing to ount for sesonlity ould led to misllotion of resouresF hile esolowskiD irhEhoenergD et lF @PHIUA look t sesonlity of movement ptterns ross uenyD kistn nd xmiiD they only onnet this theoretilly to impt on disese nd do not study the reltionship with inidene dtF pers tht hve omined sesonl moility dt from moile phones with sesonl disese inidene dtD suh s esolowskiD gF wetlfD et lF @PHISA for ruell nd esolowskiD ureshiD et lF @PHISA for dengueD hve not done so in usl frmeworkF his pper ontriutes to the existing work y iming to mesure the usl reltionship nd size of the e'et of imported mlri using liner dynmi pnelEdt model nd ontrolling for time (xed e'etsF hereforeD in ddition to the two res lredy identi(ed y the eonomis literture s neessry for mlri redution"priing nd doption of preventtive nd tretment interventions"this pper identi(es trgeting of higher risk moile popultions s thirdF hile this pper fouses on mlri elimintionD it hs implitions for other diseses whose spred hs een ssoited with trvel @edd PHITD yster PHIPDrothero IWUUD fln et lF PHHWD tukler et lF PHIID mD uhnD nd vegidoEuigley PHITAF ine trvel ptterns studied using ell phone dt ould led to the trnsmission of ny ommunile diseseD if these dt re otined for other ountries or for di'erent disesesD it is possile to replite the nlysis using the methods developed in this pperF s demonstrte how new soures of ig dt n e used to mesure externlities ssoited with trvel to develop more e'etive trgeting strtegies tht n e omined with priing nd doption poliiesF his further expnds the use of ig dt for development in res suh s riskEshring @flumenstokD igleD nd pfhmps PHITAD mesuring poverty @flumenstokD gdmuroD nd yn PHISD flumenstok PHITA nd providing redit to the poor @fjorkegren nd qrissen PHIVAF he pper egins y providing some kground nd desriing the dtF st then goes on to model the link etween mlri nd popultion movement in setion QF etion R outlines the empiril results linking trvel to mlri nd setion S exmines the ost e'etiveness of di'erent poliiesF ome roustness heks re provided in setion TD nd the pper onludes with setion UF S 2 Background and Data 2.1 Malaria Characteristics wlri is n infetious disese tht requires two hosts!humns nd mosquitoes!in order to spredF he mlril yle for P. falciparumD the prsite using IHH perent of ses in eneglD n tke severl weeks @World Malaria Report PHIRAF efter n infeted individul is it y mosquitoD there is n inution period lsting round W dys within the mosquito @uilleenD eF ossD nd F mith PHHTAF 6 sf the mosquito survives the inution periodD it n ite nd infet helthy individulD fter whih there is seond inution period within the humn of round IS dys @hF vF mith nd wuenzie PHHRD roshen nd worse PHHRAF ymptoms will pper t the end of this period nd the individul will eome infetiousF 7 gomining the two inution periodsD seondry se will tke round one month to pper fter primry seF 8 his pper fouses on the role of humn ehvior on spred of the diseseF 9 here re two hnnels through whih popultion movement n led to spred of mlri in lowE mlri or elimintion zonesF he (rst is residents of these zones who trvel to high mlri res nd eome infeted when it y infeted mosquitoesF ine mlri symptoms do not pper for round two weeksD the resident n trvel home feeling helthyF yne t the home lotionD the person n eome symptomtiD s well s infet mosquitoesF hese infeted mosquitoes n infet other individuls nd pss on the diseseF he seond hnnel is visitors or migrnts tht live in high mlri re nd trvel to low mlri reF eginD t the eginning of their trvelD these individuls might not exhiit symptomsD ut n still e rriers of the diseseFherefore if they re it y mosquito in the low mlri reD they ould infet tht mosquito nd it ould in turn infet other individulsF 6 The incubation period can vary, but two dierent sites in Senegal had an average of 9 days. 7 Unlike other malarial parasites, P. falciparum does not have the potential to lie dormant for months. 8 Details on malaria transmission can be found in Doolan, Dobaño, and Baird 2009, D. L. Smith and McKenzie 2004, Killeen, A. Ross, and T. Smith 2006, Wiser 2010 Average radius of travel for the mosquitoes that carry the malaria parasite in Senegal is only 1-2 km; therefore, mosquito movement is not considered (Russell and Santiago 1934, Thomas, Cross, and Bøgh 2013).

Health System and Malaria in Senegal
enegl is geogrphilly divided into IR helth regionsD under whih there re UT helth distritsF he min point of servie for mlri ses is the helth postF here re totl of IDPRU helth posts in the ountry @xvD sxpywD vrw PHISAF sn dditionD there re rurl helth huts nd ommunity helth workers tht provide re for those living fr from helth postD nd report the ses to the losest helth postF ine the estlishment of the xtionl wlri gontrol rogrm @xvA in IWWSD the progrm hs oordinted vriety of mesures nd poliies tht hve led to redution in deths ttriuted to mlri from IPFWQ per IHHDHHH people in PHHH to VFPT in PHIQ @xvD sxpywD vrw PHISAF gurrentlyD the north of the ountry hs very low inidene nd is t the level onsidered redy for elimintion y the orld relth yrgniztion @I se per IHHHD known s the preEelimintion phseAF sn ontrstD the south still hs high se lodD with some distrits s high s PUH ses per IHHHF 10 he heterogeneity n e prtly ttriuted to environmentl ftors euse the riny seson is twie s long in the south s in the northD whih llows for mosquitoes to reed nd spred the disese for longerF xeverthelessD the mosquitoes required to spred the disese re lso present in the low mlri res @xdith et lF PHIPAF qiven the two distint zones in the ountryD the qovernment of enegl strives to ontinue reduing the se lod in the outhD while iming to eliminte it ompletely from the xorthF es potentilly infeted individuls trvel from the outh to the xorthD thoughD they n hinder elimintion e'orts in the xorthF 2.3 Population Movement in Senegal enegl hs lrge )ows of long term nd permnent migrtionD with PU7 of the popuE ltion reorded s n internl migrnt in PHHR @F hF pllD grreteroD nd wF F rr PHIHAF 11 e lrge prt of this migrtion is rurl to urn due to irregulrity of rinfll nd degrdtion of the eosystems tht hve impted griulturl tivity @F hF pllD grreteroD nd wF F rr PHIHD qoldsmithD qunjlD nd xdrishiknye PHHRAF sn turnD this longer term migrtion n led to ommuting ptterns s people return home to visit fmily nd friends or reeive visitors from home @ghoD wyersD nd veskove PHIIAF pousing on migrnts in hkrD eF F pll @IWWVA (nds tht VU7 of mle nd VI7 of femle migrnts visited their home resD with the mjority of visits ourring for holidysD fmily eremonies nd religious festivlsF hetiled studies of the tol ethni group in severl villges (nds tht irulr migrtion plys n importnt roleD with over VH7 of unmrried tol youth trveling to the ities in ytoer nd then oming k efore the rie hrvest in tuneEtuly @vinres PHHQAF froder reserh on youth in enegl hs shown tht more thn hlf of the internl migrtion they engge in is temporry nd rurl to rurl or urn to urn @rerrer nd hn PHIQAF edditionlly there re still pstorl groups tht trvel within set territory@edrinsen PHHVAF nderstnding the movement ptterns within enegl is importnt for thinking through potentil onfounding ftors etween movement nd mlriF he mjority of the literture points to movement triggered y griulturl sesons s well s holidysF hese ftors nd their reltionship to mlri inidene will e disussed in the model setionF sn eneglD P7 of the popultion re interntionl migrnts while only IFP7 of the popultion emigrted from eneglF pousing on immigrtion into enegl in PHIQD only HFPQ7 of the popultion entered the ountryF hile the pper fouses on the role of internl migrtionD the potentil impt of interntionl migrtion will e disussedF 2.4 Malaria Data vowEinidene res lose to elimintion n experiene the lrgest externlity from popultion moility for three key resonsX @IA without these trvelers the disese ould e redued to zero nd require lower government expendituresY @PA in high mlri resD people hve usully uilt up n immunity to the diseseY thereforeD trveler entering high mlri re is less likely to led to new infetion even if he or she infets dditionl mosquitoes V in the reD while in low mlri re immunity does not existY nd @QA the infetion in lowEmlri re is likely to e more severe due to the lk of exposure to the diseseF hereforeD s fous on the prt of enegl disussed erlier tht is t preEelimintion stgeF ithin this reD s fous on (ve of the lowest mlri distrits where dt re disggregted t the helth post level nd ville for every helth post in these distritsF wlri dt re not ville t this high sptil resolution for ny of the other low mlri distritsF he dt over IIU helth postsF he ppendix provides mp of the (ve helth distritsD whih s sudivide into res sed on the lotion of the helth posts nd ell phone towersF relth posts in lose proximity were grouped together forming QT helth post thment resF s use inidene dt sed on dt olleted from eh helth post on ll new ses in the reporting monthF 12 he use of inidene dt is one thing tht seprtes this pper from some of the previous work tht relies on endemiity dtF he endemiity dt re gthered from prsite rte surveys in whih rndom susmple of the popultion is tested for mlri prsitesF hen the mlri prevlene is very lowD the likelihood of hving positive se eomes very smllF hereforeD when fousing on lowEmlri setting to understnd impt of moilityD inidene is more relile mesure @elegn et lF PHIQD tF wF gohen et lF PHIQAF xv9s work hs led to system tht provides high qulity dt on mlri inidene ross the ountryF sn eneglD if n individul feels sikD usully experiening feverD hills nd ftigueD she will go to the losest helth post where she will e tested using rpid dignosti test @hA due to her symptomsF sf she tests positiveD she will e provided with medition for free to tret the diseseF hereforeD ll inidene dt used in this pper omes from suspeted ses tht hve een tested nd re positive for mlri sed on the testF por the rest of the ountryD these inidene dt re ville monthly t the helth 12 The data used to measure malaria incidence comes from the PNLP and PATH, a non-prot organization working with the PNLP to ght malaria in Senegal through its Malaria Control and Elimination Partnership in Africa (MACEPA). pigure IX everge wonthly relth post gthment ere wlri snidene per IHHH nd everge wonthly infllD tn PHIQEhe PHIS y relth histrit distrit levelF hese dt re used to lssify the risk of trvelers sed on their originF wonthly mlri inidene per IHHH people is verged ross helth post thment res within distrits for three yers in pigure IF histrits on verge hve round HFI ses per IHHH people per monthF he (gure overlys the monthly umultive rinfll in entimeters verged ross helth post thment resF 13 he omprison of ses nd rinfll demonstrtes strong sesonlity of mlri in enegl nd the lose reltionship etween rinfll nd mlriD with the pek of ses nnully ourring one to two months fter the pek in rinfllF s model this reltionship in the nlysis sine rinfll n e orrelted with oth mlri nd popultion movementF here re three min hllenges tht rise with using linil dtX inomplete dt reportingD presumptive dignosis sed on symptoms rther thn testing nd nonEutiliztion 13 Rainfall data are from the Climate Prediction Center (2016) Rainfall Estimator for Africa. of the puli helth system @elegn et lF PHIQAF sn the dt only IP out of IDRIT helth postEmonth oservtions re missing in PHIQF sn dditionD WW7 of suspeted ses were tested prsitologilly in the (ve distrits nlyzedF ine oth mlri ses nd imported ses re lulted sed on se dtD s long s utiliztion is reltively uniform ross the ountryD it should not is resultsF fsed on the hr dt for ll the regionsD helth fility ws visited for fever in hildren under ge S in RT7 of ses @exh nd sgp snterntionl PHISAF he stndrd devition of this utiliztion ross regions is TFS perentge pointsF hile in the min nlysisD s ssume uniform utiliztionD s inlude roustness hek where ses re sled y regionl utiliztion in the hrF 2.5 Population Movement Data he dt used to mesure short term movement ome from phone reords mde vilE le y ontel nd yrnge in the ontext of the ht for hevelopment ghllenge @wontjoye et lF PHIRAF he dt ome from the seond phse of the ghllenge nd onsist of IS illion ll nd text reords for enegl etween tnury ID PHIQ nd heemer QID PHIQ for ll of ontel9s user seF 14 he dt ontin informtion on ll lls nd texts mde or reeived y sw rdD their timeD dte nd lotion of the losest ell phone towerD whih enles trking of sws in spe s they mke lls from di'erent tower lotionsF he dt re nonymizedD with rndom sh provided tht mkes it possile to trk the sme sw over timeD ut no identifying informtion on the individulsF yn verge there re IDTSU lls or texts per sh during the yerD nd on verge n sh hs ll or text on ISS dysF ih tower is ssigned helth distrit sed on its q oordintesF s follow previous literture to ssign individuls dily helth distrit lotion sed on the ell tower of the lst ll or text of the dy @uktnonhi et lF PHITAF sn instnes where there re dys with no llsD s replite esolowskiD igleD et lF @PHIPA nd ssign the helth distrit lotion of the dy losest to the one missingF 15 e helth distrit lotion is ssigned to eh sw 14 At this time it was not possible to obtain more recent data or data from other providers. 15 The appendix includes a robustness check where observations with more than 14 days in a row missing for every dy of the yerF wovement is de(ned s hnge in lotion from one helth distrit to nother etween two onseutive dysF he popultion is highly moileD with over VH7 of ll ontel sw rds tking t lest one trip nd over qurter million trveling on verge on ny given dyF yn verge nnully per sw there re IH di'erent trips to lmost (ve di'erent helth distritsF sn ddition to ssigning the towers within the study re to helth distritD s ssign them to helth post thment re sed on their q lotionF hereforeD eh trveler entering one of the (ve helth distrits is ssigned spei( helth post thment re sed on the lst ll or text of the dyF 16 nel of pigure P shows the verge numer of people entering helth post thE ment re eh dy s perent of the popultion in tht thment re verged ross ll resD long with vertil lines mrking severl religious holidys nd importnt pilgrimgesF he movement ptterns lrgely lign with the holidys nd pilgrimgesD whih supports the (ndings in eF F pll @IWWVA tht the mjority of migrnts to hkr visit their home re primrily for holidysD religious festivls nd fmily eremoniesF yn verge for ll the helth post thment resD round Q perent of the popultion of tht re enters on ny given dyF he vrition in perent of people entering n vry widely y helth post thment re nd dte within distrit @nel fAF por helth post thment res where n imporE tnt religious leder residesD on ertin religious holidys the numer of people entering is lose to or over SH7 of the popultion of the reF por other helth postsD the eginning of ertin griulturl sesons or other holidys led to lrge jumps in people enteringF his vrition mkes it possile to study the impt of people entering on mlri ses in these res tht re otherwise geogrphilly lose together nd very similrF sn PHIQD ontel hd slightly over WFS million unique phone numers on its network while the popultion of enegl ws IQFS millionFhere re two sets of people tht re potentilly exluded from the dt nd need to e ounted for!those without phone nd those with are removed. 16 Movements within a district between health post catchment areas are not counted. 3 Empirical Model he empiril spei(tion is derived from model of mlri tht is sed on previous models used in hF vF mith nd wuenzie @PHHRAD gosner et lF @PHHWA nd orresEorndo nd odriguez @IWWUAF pour key ssumptions llow me to simplify the model so tht inidene in the urrent month is dependent on inidene in the lst month using liner funtionl formF ixpeted imported ses enter s liner dditive term s in orresEorndo nd odriguez @IWWUAF he modelD ssumptions nd implitions re desried in detil in epE pendix eF s strt out estimting eqution I using yvD with imported inidene lulted using eqution PX originF he mtrix Z it inludes zeroD one nd two lgs of rinfllD whih pture oth the griulturl sesons tht ould in)uene movement nd hnges in mlri inidene due to 19 I use the detailed knowledge of the timing from the mobile phone data to factor in how many of the 15 days were in month t and how many in month t − 1 and use the incidence both in month x jt and x jt−1 to determine the probability the person is infected. environmentl ftorsF edditionl funtionl forms of rinfll were lso tested ut did not signi(ntly hnge the nlysisY thereforeD liner funtionl form ws used for rinfllF 20 it represents idiosynrti shoksF s luster errors t the helth post thment re level to ount for the ft tht errors re orrelted within pnelsF 21 he min oe0ients of interest re β 1 nd β 2 D whih represent the numer of seondry ses generted y infeted trvelers nd the numer of primry mlri ses imported y infeted trvelersF 3.1 Identication por my identi(tion to e orretD it is neessry tht within helth post thment re over timeD ny idiosynrti shoks in mlri inidene re not orrelted with expeted imported mlri inideneF egriulturl sesons nd holidys re the two mjor resons for trvelF egriulturl sesons re orrelted with rinfllD nd dditionllyD rinfll ould 'et the onditions for trvel @qulity of rodsAF s ontrol for this potentil onfounder y inluding rinfll ovrites in my spei(tionF st is lso possile tht holidysD whih inrese popultion movementD ould 'et mlriF eople might spend more time outside during the holidys nd e exposed to mosquitoesF s ddress this potentil thret to identi(tion using pleo test where s sle trvelers y verge monthly inidene in the ountry rther thn y the inidene of their originF s lso exmine the reltionship etween pst nd future imported ses nd urrent mlriF pinllyD the dynmi pnel model with reltively short pnel of IP time periods ould introdue is if the error term is mehnilly orrelted with the lgged dependent vrile on the right hnd side @xikell IWVIAF s study this y ompring the (xed e'ets model with rndom e'ets modelF qiven the results of this omprisonD the preferred spei(tion used is n ugmented version of the erellnoEfond qenerlized wethod of woments estimtor designed to ddress situtions with smll D lrge x pnelsF 20 The appendix includes results with these dierent specications. 21 I include a robustness check with spatial and panel autocorrelated standard errors.

Quantifying the Eect of Imported Cases
ih imported se of mlri is ssoited with IFPQ ses of mlri in the urrent period nd HFQQH ses in the next period sed on the (xed e'ets model @golumn I of le IAF his spei(tion ssumes the externlity from lolly generted nd imported ses will e the smeF s expliitly test this y inluding lgged imported inidene long with lgged nonEimported inidene @golumn PAF he oe0ient on lgged imported inidene is not signi(ntly di'erent from the oe0ient on lgged lol inideneD whih implies tht there is no di'erentil e'et etween lgged imported nd lgged lol inideneF s estimte rndom e'ets model to test if there ould e dynmi pnel is due to the inlusion of (xed e'ets with reltively short pnel @golumn Q of le IAF he oe0ient on imported inidene is smllerD while the oe0ient on lgged inidene is lrgerF sn using rndom e'etsD thoughD s m no longer ontrolling for timeEinvrint hrteristis of the helth post res tht ould e orrelted with oth imported inidene nd mlri inideneF s inlude severl hrteristis of the helth fility resD inluding popultion densityD dummy for urn resD nd dummy for helth fility res tht re not long the order of the ountry @golumn RAF snluding these ovritesD the oe0ient on imported inidene is igger nd loser to the oe0ient from the (xed e'ets modelF e rusmn test ompring the two models (nds they re signi(ntly di'erentF qiven eh model hs potentil to e isedD sine the (xed e'ets model might hve some dynmi pnel is while the rndom e'ets model might hve omitted vrile isD s use n erellnoE fond spei(tion @golumn S of le IAF fsed on this modelD for eh imported se of mlri per IHHHD there re IFHW ses per IHHH reportedF sn dditionD for eh lgged se per IHHHD there is n dditionl HFSTQ of se generted the following monthF his lso represents the negtive externlity of n imported se the previous monthF he epidemiologil model tht the empiril spei(tion is sed on leds to severl  The orange dash lines represent the monthly predicted malaria incidence averaged across health post areas within a district. This was calculated based on values for the parameters of the model drawn from their distributions. I conducted 500 replications and used the mean monthly incidence value per health post area. Panel a compares the predicted values to the actual malaria incidence, where the solid green line is actual incidence averaged across health posts within a district. In panel b, the predicted incidence is compared to a scenario where no cases were imported by travelers, shown in dashed blue lines. Incidence with 0 imported cases was calculated using the same 500 replications for parameter values, but imported cases were set to 0.

Mechanism Evidence
s now provide some dditionl evidene of the usl impt of imported inidene on totl inideneF pigure R shows oe0ients from regression of mlri inidene on two lgs nd two leds of imported inideneD long with lotion nd time (xed e'ets nd rinfll ontrolsF wlri inidene two months erlier nd one month erlier hs no reltionship with imported ses in the urrent periodF wlri inidene in the urrent period nd one month lter re ssoited with imported inideneD s oth of those oe0ients jumpF smported inidene does not seem to hve signi(nt impt on inidene two months lterF 23 ine the smple size is muh smller fter inluding the leds nd lgsD the stndrd errors re lrgerF xeverthelessD the trend in the size of the oe0ient still demonstrtes tht future imported inidene does not drive urrent mlri inideneF s ondut severl pleo tests to refute potentil lterntive explntions nd ompre them to the min spei(tion @le PAF yne lterntive explntion is tht imported inidene is orrelted with periods of higher trvel suh s religious holidysD nd these holidys ould lso e positively orrelted with mlri for resons unrelted to trvelF huring religious holidys people might spend more time outside nd re more likely to e it y mosquitoesF o test thisD rther thn using the inidene of the lotion person is oming from to lulte their proility of importing mlriD s use the verge monthly inidene ross ll helth distritsF sn this wyD the lotion of where trvelers enter from no longer 'ets the vrileD only the trvel ptterns doF here is no reltionship etween this lterntive vrile nd mlri inidene @golumn PD le PAF st is possile tht only the inidene of the origin mttersF por exmpleD if the origin of trvelers hs similr inidene to the destintionD the vrile of interest my pture this orreltion etween origin nd destintion irrespetive of trvelF o test thisD s lulte expeted imported inidene sed on the inidene of the originsF ther thn seprtely 23 I would not expect a persistent eect of imported cases two months out because the malaria season when the necessary mosquito vector is present in these areas is very short, lasting only around 3 months; therefore, there is not enough time for tertiary cases to develop due to the month long incubation periods. pigure RX istimted smpt of putureD gurrent nd st ixpeted smported wlri sniE dene Notes: The gure was constructed based on a regression of current malaria incidence on imported incidence of malaria two months later, one month later, currently, last month and two months ago, controlling for time and location xed eects and rainfall covariates and clustering errors at the health post area level.

Malaria Policies Toward Travelers
he xqy er hs spei(lly foused on reduing imported ses in the distrit ihrd ollF hey hve used volunteers in the ommunity to lert helth workers to the rrivl of new trvelersF relth workers trk down these trvelers nd sk to test them using n hD nd tret those tht test positiveF fsed on PHIS dt provided y the ihrd oll relth histrit hiretorD QDTHW people were identi(ed s trvelersD of these QDQVT were tested nd IH tested positive for mlriF sn PHISD there were totl of IVT imported sesY thereforeD this strtegy ws only le to detet S7 of imported sesF 25 e more systemti poliy to trget trvelers ws implemented in one helth post in ihrd ollD whih is privtely run y the eneglese ugr gompny @gA for its workers nd their fmiliesF g hires over QHHH migrnt workers every yer to help with the sugr hrvestF wlri ws lrge urden for the ompnyD using lower produtivityD high senteeismD nd high spending on phrmeutils to tret it @hjio nd xdiye PHIQAF sn lte PHIID the g implemented new mndtory poliy for ll sesonl workersX testing every worker t the eginning of the seson using n hD treting nyone testing positiveD nd providing workers nd their fmilies with ednets nd informtionF here ws drsti derese in ses fter the implementtion of this poliyD with se numers t zero or lose to zero fter the poliy @pigure SAF ht on two types of shistosomisis mong workers t the g show no drop in those diseses fter lte PHIID demonstrting tht the drop in mlri nnot e ttriuted to n overll improvement in the helth re filityF his losely mirrors the outomes mesured y hillonD priedmnD nd erneels @PHIRAD who (nd tht poliy o'ering testing nd mlri tretment for workers t sugrne plnttion in xigeri leds to IH7 inrese in ernings due to inresed lor supply nd produtivityF e strtegy to derese mlri ses tht ould e hrnessed for trgeting trvelers is protive ommunity tretment @roegA implemented y trined home re providers @rgsAF he pilot of this intervention onsisted of rgs going doorEtoEdoor weekly to 25 Data on imported cases is based on surveys conducted in Richard Toll. pigure SX i'et on wlri gses of oliy rgeting wigrnt orkers t the eneglese ugr gompny Notes: The gure shows number of cases of malaria and two types of schistosomiases seen at the health post of the Senegalese Sugar Company. The red vertical line marks the timing of when a new policy was implemented by the company that tested every migrant worker for malaria and treated those that tested positive. Data was provided by the CSS. every household in villgeD heking for individuls with symptomsF gompred to villges tht did not reeive roegD the odds of symptomti mlri were QH times lower in the intervention villges @vinn et lF PHISAF his type of poliy ould e pplied to res tht reeive trvelers during the weeks when the most expeted infetions enterF pinllyD just s moile phones n e used to mesure ggregte movement ptterns to improve trgetingD they ould lso e used more diretly for the trgetingF woile phones re lwys linked to tower if they re turned onY thereforeD the provider knows s soon s n individul hnges towersF en innouous poliy ould e to llow users to opt into n informtion progrm tht sends trgeted text messge s soon s someone tht hs opted into the progrm hnges lotion from high mlri tower to low mlri towerF he messge ould reommend nd provide n inentive to get tested t the losest lini for freeF nd insted the poliy were to test every single trveler oming into the S preEelimintion distrits tht re the fous hereD it would men testing TDWSTDIWU trvelers in PHIQ sed on the sled moile phone dtF sf eh trveler were suessfully tested so tht ll trvel ses of mlri were foundD tretedD nd seondry infetions were preventedD it would men TTQ ses treted or preventedD representing round RR7 of totl ses in this reF iven just tking the ost of n h to test eh person @6HFSHAD without dding ny other osts PV ssoited with suh n interventionD it mounts to round 6SDQHH per seF gompred to typil enhmrk for ostEe'etiveness of 6ISHD trgeting ll trvelers would e QS times s ostlyF hereforeD if poliy were to trget trvelersD only suset should e trgetedF here re two wys tht poliy n e trgetedX @IA it n trget ertin destintion res for trvelers or @PA it n trget trvelers from spei( origin resF por oth ses there re two sets of ostsX @IA (xed ostD whih onsists of trining ommunity helth workersD helth post nursesD nd distrit helth supervisors in investigtion of trvel ses s well s osts for weekly eletroni dt trnsmissionY nd @PA vrile ostD whih re the osts ssoited with investigting nd treting trvelersF 26 s use the pisl er PHIS wlri ypertionl ln for enegl for the poliy simultionsF fsed on this plnD 6RHHDHHH ws lloted for se investigtion nd trgeting individuls in distrits with inidene less thn SGIHHHF qiven there were IW suh distrits in PHISD s ssigned the funding proportionl to distrit popultion in order to ssign n mount to the (ve distrits tht re prt of the simultionF his leds to 6IPUDVSH dedited to the (ve low mlri distrits studied hereF s ssume n even split etween (xed nd vrile ostsF o lulte the vrile ost per personD s use the informtion ville from ihrd oll where QDTHW people were trgeted in PHISF rile funding for tht distrit of 6IHDPVT leds to per person ost of 6PFVSF he (rst type of trgeting fouses on destintion resF qiven some set of resoures ment to trget trvelersD those resoures n either e distriuted ross ll helth filiE ties or they n e onentrted in smller set of filities in ertin res nd in ertin monthsF he most nive method for trgeting would e to rndomly selet helth fility res nd months nd trget ll trvelers in the resGmonths rndomly seletedF his is in e'et equivlent to not trgetingF sn prtie this would never e done sine t minimum poliymkers know when mlri is most prevlent nd would not trget trvelers during months the ountry is e'etively mlriEfreeF hereforeD seond strtegy would e to trE get rndomly ertin helth res during the months of high mlri prevlene (rst @eugust 26 For simplicity, I assume the variable cost scales proportionally with the number of travelers. to heemerA nd then during the low mlri prevlene monthsF ith the informtion ville t hndD poliymkers ould do even etter in trgeting y using informtion from the previous yerF hey know whih helth fility resGmonths hd the highest level of mlri in the previous yer nd n trget helth fility res in months ording to their ordering the previous yerF he ell phone dt llow for even more e'etive trgetingF he piee of informtion urrently not ville to poliymkers is the numer of trvelers entering n re from ny given other distrit in the ountryF he ell phone dt provide this informtion nd omined with the inidene from PHIPD it mkes it possile to estimte whih helth fility res re most t risk from trvelers in ertin monthsF his n e espeilly e'etive euse trvel hoies re not rndomF here re often high movement orridors etween ertin ommunities in ountryF hereforeD it is likely tht there re pokets tht will e more 'eted y trvelers oming from high mlri res thn other prts of the distritF fy fousing on the pokets of res most 'eted y trvelers from high mlri settingsD limited resoures n e spent more e'etively trining helth professionls nd trking trvelers only in these resF pigure T demonstrtes the full ost urvesD from strtegy where only one helth distrit reEmonth is tretedD ll the wy up to ll helth distrit reEmonths eing tretedF he ene(t t eh point is lulted sed on the erlier model to lulte the totl primry nd seondry ses ttriuted to trvelersF s ssume tht ll trvelers re trgetedD ut only WR7 of them gree to tke the test nd ontriute to the ene(t from trgetingF 27 hepending on the resoures ville to the governmentD it is possile to determine for ny given udget how mny ses would e treted or verted depending on the trgeting strtegy hosenF vooking ross the entire distriution in the top pnelD the trgeted strtegy sed on informtion from moile phones is onsistently the most ostE e'etive oneF eross the whole distriutionD the ell phone dt sed trgeting poliy performs IIFIS7 etter on 27 This is based on data from Richard Toll where 3,386 out of 3,609 targeted travelers agreed to be tested. verge ompred to the next est poliy of using informtion on inidene from the yer eforeF ooming in on the prt of the distriution up to 6RHHDHHHD the mount spent on this type of progrmD the ell phone dt trgeted poliy performs over QHH7 etter on verge @nel D pigure TAF he seond type of trgeting fouses on trvelers from prtiulr origin resF his is more di0ult in terms of implementtion euse it requires the ility to identify trvelers oming from spei( resD ut hs the potentil of eing more ostEe'etive sine resoures re foused on the highest risk trvelersF s se the trgeting strtegies on the distrit the individuls re oming from nd the month in whih they re trvelingF hereforeD if distritEmonth is hosen s reeiving trgetingD then every person trveling from tht disE trit to the preEelimintion re in tht month would e treted with the poliyF s ssume gin tht WR7 of trgeted trvelers re tested sed on the experiene in ihrd ollF pour strtegies re gin ompredX @IA the implusile one of the government rndomly hoosing distritEmonths @nonEtrgetingAY @PA the government hoosing distritEmonths rnE domly within the mlril seson nd then during the rest of the yerY @QA the government using monthly mlri inidene in the prior yer to order the distritEmonths from those with the highest to the lowest inideneY nd @RA ostEene(t vlue is lulted for eh distritEmonth sed on the numer of trvelers nd the vrile ost nd uses inidene from the previous yer to lulte the totl impt of the imported ses @the ene(tAF nel of pigure U shows the ost urves for these four strtegies zoomed in on the relevnt udget of 6RHHDHHHF xote tht the ost strts t 6TQDWPVD whih is the totl (xed ost for ll the filities in the (ve distritsD sine it is ssumed tht trining nd preprtions re done ross ll helth fility res ut only prtiulr trvelers re trgeted ross these resF sing the ell phone dt to inform trgeting leds to higher ost e'etiveness thn the next est strtegy sed on the government using inidene from the previous yer to trget trvelers from spei( lotionsF sn prtiulrD t udget of 6RHHDHHH it performs PU7 etter on vergeF nel ompres trgeting of spei( trvelers entering ll (ve QI pigure TX rgeting eresX gost nd fene(t nder hi'erent trtegies (a) Full Cost Curve (b) Cost Curve Zoomed in on Less than $400,000 Notes: The panels show four dierent strategies for targeting travelers. Each symbol represents a health facility area-month. Targeting a specic health facility area-month means targeting all travelers entering that health facility area in that month. The strategies lay out which health facility area-months are targeted rst. The cost is calculated based on a variable cost of $2.85 per traveler and a xed cost of $63,928 split proportionally between health facility areas based on population and number of facilities. The benet is based on the parameters of the model to calculate the number of primary and secondary cases generated by travelers from each district in each month and summed for all travelers in a given health facility area month. It is assumed that only 94% of those targeted are successfully tested. low mlri distrits @type PA to trgeting ll trvelers tht enter only spei( helth post thment res in those (ve distrits @type IAD using the ell phone dt for othF rgeting spei( trvelers rther thn only res is PSU7 more e'etive with udget of 6RHHDHHHF he previous senrios onsider either trgeting prtiulr trvelers or trgeting prE tiulr resD ut it is possile to omine the two types of trgeting to trget prtiulr trvelers going to prtiulr res in ertin monthsF his would not e possile without the ell phone dtD whih provides extremely grnulr informtion on sptil movement of individuls ross time so tht we know how mny trvelers enter spei( re in given month nd this n e used to lulte the ost of trgeting eh of these trvelers nd the ene(t of quikly identifying nd treting ny ses they my hve rought through trvelF pigure V shows the ost urve in this senrio where trvelers from prtiulr distrit to prtiulr helth fility re re trgeted in spei( monthF 28 his urve is ompred to the previous urves of just trgeting trvelersD just trgeting resD nd lso the est strtegy without using ell phone dt of trgeting trvelers sed on inidene in PHIPF rgeting oth trvelers nd res leds to SP7 etter performne on verge ompred to the nonEell phone dt strtegy when fousing on udget of under 6RHHDHHHF sing ell phone dt for trgeting oth trvelers nd res ompred to just trgeting trvelers is IW7 more e'etive on verge with udget under 6RHHDHHHF here re two importnt limittions in onduting this type of trgetingF he (rst is relted to potentil risk of trgeting res sed on movement informtion from previous yerD given tht popultion movement ptterns my hnge drstilly from one yer to the nextF yther reserh tht hs used ell phone dt for severl yers in xmii (nds very onsistent short term movement ptterns ross three yers @wilushev et lF PHIUD esolowskiD irhEhoenergD et lF PHIU AF edditionllyD if short term movement mtries from ell phone dt were mde ville to poliymkers on n ongoing sisD it would e possile to djust trgeting in rel time s informtion eomes villeF 28 The xed cost of an area is added when the rst set of travelers in a month is treated in that area. pigure UX rgeting rvelersX gost nd fene(t nder hi'erent trtegies (a) Cost Curve Zoomed in on Less than $400,000

(b) Comparing Targeting Travelers and Targeting Areas
Notes: Panel (a) shows four dierent strategies for targeting travelers. Each symbol represents a districtmonth. Targeting a specic district-month means targeting all travelers entering the ve low malaria districts from that district in that month. The strategies lay out which district-months are targeted rst. Panel (b) compares targeting of specic travelers entering all ve low malaria districts to targeting all travelers that enter only specic health post catchment areas in those ve districts, using the cell phone data for both. The cost is calculated based on a variable cost of $2.85 per traveler and a xed cost of $63,928 split proportionally between health facility areas based on population and number of facilities. The benet is based on the parameters of the model to calculate the number of primary and secondary cases generated by travelers from each district in each month and summed for all travelers in a given health facility area month. It is assumed that only 94% of those targeted are successfully tested. pigure VX rgeting foth rvelers nd eres gompred to hi'erent trtegies Notes: A scenario where travelers from a particular district to a particular health facility area are targeted in a specic month is compared to previous scenarios of targeting particular health facility areas, targeting travelers from particular districts, and the best-case scenario if no cell phone data is available of targeting travelers based on the incidence of districts in the previous year.
he seond limittion reltes to representtiveness nd who my e missed through these trgeting strtegies @flumenstok PHIVAF he movement ptterns of the lowest inome re likely missing from these dt due to lk of moile phoneF hereforeD this type of trgeting my miss mrginlized res tht my experiene importtion of mlri from very low inome groups tht re not ptured in the movement ptternsF sf moile phone dt trgeting strtegies re implemented y poliymkersD it ould led to mrginlized pokets of mlri in the elimintion zones due to lk of trgeting to the res reeiving the lowest inome trvelersF vukilyD elimintion zones hve in ple surveillne systems t helth filities tht trk mlri ses tht ome to the filityF husD it will e possile to nlyze the dt for outlier helth filities tht do not experiene derese in mlri fter the trgeting strtegies re implementedF p to nowD high mlri distrits from where ses re imported hve not een disE ussedF sf mlri were redued signi(ntly in those distritsD it would utomtilly redue importtionF he ssumption is tht while strtegi trgeting is done in the lowEmlri zonesD in the highEmlri distritsD pkge of interventions imed t reduing the urden of the disese is mintinedF his is in line with the ry strtegy for mlri elimintionF QS 6 Robustness Checks s do severl roustness heks to test the min spei(tion @le QAF golumn P uses n estimte of imported inidene without weighting the moility dt to e representtive of the full popultionF his ssumes tht the only movement in the ountry is the movement in the ontel dtD whih would e n underestimteF eighting the dt represents n upper ound for the level of movementF he tul movement tht oursD nd thereforeD imported inideneD is then somewhere in etween these lower nd upper oundsF hus the rel e'et should lso lie etween these upper nd lower ounds of PFI nd IFUF sn ddition to weighting the movementD golumn Q sles oth imported inidene nd totl inidene y helth post utiliztion t the region levelF he results re similr nd not signi(ntly di'erent from the results in the min spei(tion @golumn IAF tiliztion is reltively uniform throughout the ountryY thereforeD inorporting utiliztion does not signi(ntly hnge the resultsF s rerun the spei(tion using gonley stndrd errors tht ount for sptil utoorreltion nd seril utoorreltion over time @golumn RA @rsing PHIHAF 29 he results remin signi(ntF sn golumn SD s use net imported inideneD sutrting expeted infeted trvelers levE ing the helth post thment reF foth the oe0ients on imported nd lgged imported do not hnge signi(ntly nd they remin signi(ntF esults from dditionl roustness heks re ville in eppendix fF hese inlude @IA using ses rther thn inideneY @PA djusting the popultion tht inidene is sed on y the numer of people entering nd leving the re eh monthY @QA loosening the ssumption tht the suseptile populE tion is equl to I nd sling lgged inidene y lulted suseptile popultionY nd @RA restriting the movements inluded in lulting imported inidene y removing ny movement where the sw rd hd no lls or texts for more thn two weeks efore or fterF yne limittion of the moile phone dt is tht it only inludes moility within enegl nd nnot inorporte interntionl migrtionF smmigrnts oming in from high mlri 29 I use a 30km cuto for the spatial correlation and two lags for the autocorrelation. ountries s well s emigrnts returning nd visiting fmily from high mlri settings ould oth impt mlri inideneF here re detiled se dt ville from ihrd oll distrit where eh se ws investigted nd trvel informtion ws inluded on the infeted individul sed on survey dtF yut of ITI sesD there re W ses where the trveler ws from outside of eneglD or only SFSW7 of sesF he smll impt of interntionl migrtion likely rises from the ft tht while some of enegl9s neighors suh s wli hve higher mlri inidene @VW ses per IHHHAD the only interntionl order ner the preEelimintion distrits studied here is wuritniD whih hs lower inidene rte thn northern enegl of only HFR ses per IHHHF xeverthelessD future work ould try to inorporte the impt of hue to the twoEhost systemD mlri is modeled using two di'erentil equtions to desrie the dynmis of infeted humns nd infeted mosquitoesF hese were (rst modeled y F oss @IWIHA nd then expnded y wdonld et lF @IWSUAF he model used in this pper is ossEwdonld type model sed on models used in hF vF mith nd wuenzie @PHHRAD gosner et lF @PHHWA nd orresEorndo nd odriguez @IWWUAF here re two stte vriles nd the model is usully expressed in ontinuous timeD lthough hereD s will present it in disrete timeF he stte vriles re y it D the frtion of mosquitoes infeted in lotion i t time t nd x it D the frtion of humns infeted in lotion i t time tF sn the model extension here tht inludes the impt of popultion movementD ses n either e generted lolly in lotion i or imported from ny other lotion j into iD I i F es modeled y orresEorndo nd odriguez @IWWUAD imported ses enter the model linerlyF vol ses in lotion i re generted sed on the suseptile popultion nd severl iologil prmetersF he suseptile popultionD S it−w D is the frtion of the popultion tht is suseptile to mlri t time t − wD where w is the totl prsite inution periodF he other prmeters re the trnsmission e0ienies from infeted mosquitoes to humns nd humns to mosquitoesD b it−w nd c it D the numer of ites on humns per mosquitoD a it−w nd the rtio of mosquitoes to humnsD m it−w F he hnge in the numer of infeted humns nd mosquitoes is desried yX where µ it is the mortlity rte of mosquitoes nd τ it is the inution period from the time mosquito eomes infeted until it is infetiousF he prmeter r i is the reovery rte of humnsF s mke four ssumptions rising from the epidemiology literture sed on modeling the system in low mlri settingX IF he totl prsite inution time is one month sed on the mlri yleF PF he mosquito popultion is t the stedy stte sine mosquito popultions hve reltively rpid turnover 30 QF ell mlri ses in month t re treted immeditely nd reover in month tF 31 RF fsed on hF vF mith nd wuenzie @PHHRAD when the proportion of infeted huE mns is smllD the numer of infetious ites reeived per dy y humn @known s the entomologil inoultion rteD tking the form EIR it = m it a 2 it c it e −µ it τ it x it µ it +a it c it x it A n e pproximted y c it C it x it D where C it is the expeted numer of humns infeted per infeted humn per dyD ssuming perfet trnsmission e0ieny @b it = c it = 1AD known s the vetoril pityF he ssumption pplies euse the nlysis is onduted 30 According to the CDC, adult female mosquitoes, which spread malaria, do not live more than 1-2 weeks in nature (Center for Disease Control 2015). 31 The incidence data in the analysis is based on diagnosed cases, which are provided with free antimalarial treatment upon diagnosis. The literature shows that within a few days of treatment the majority of parasites are eliminated (Nosten andNicholas J White 2007, N. White 1997).
in low mlri settingF pigure fFI provides evidene tht the ssumption holds for these dtF fsed on ssumption ID s set w = 1F fsed on ssumption PD s solve eqution Q for the qusiEequilirium proportion of infetious mosquitoes s hs een done in hF vF mith nd wuenzie PHHR nd uktnonhi et lF PHITX y it−1 = a it−1 c it−1 x it−1 e −µ it−1 τ it−1 µ it−1 + a it−1 c it−1 x it−1 @SA essumption Q implies the reovery rteD r i D is equl to one sine ll infeted individuls reover within the sme monthF his llows me to fous on new ses of mlri in month tF ine immunity does not develop in low inidene resD nyone who is not urrently infeted is suseptile to the diseseD whih implies tht the suseptile popultion is I if everyone reoversF ewriting eqution R to inorporte the implitions of ssumptions IEQX fsed on ssumption RD eqution T n e rewritten sX essumption R is importnt euse y rewriting EIR it−1 s c it−1 C it−1 x it−1 D s expliitly inorE porte the impt of the inidene lst monthD x it−1 D on the inidene in the urrent month using liner funtionl formD whih helps me pproximtely estimte the seondry ses generted this month y ses lst monthF st is then possile to estimte this model using yv s desried in the min text of the pperF