Spread of Zika in the Americas

Qian Zhanga, Kaiyuan Suna, Matteo Chinazzia, Ana Pastore y Pionttia, Natalie E. Deanb, Diana Patricia Rojasc, Stefano Merlerd, Dina Mistrya, Piero Polettie, Luca Rossif, Margaret Braya, M. Elizabeth Hallorang,h, Ira M. Longini Jr.b, and Alessandro Vespignania,f,1

aLaboratory for the Modeling of Biological and Socio-technical Systems, Northeastern University, Boston, MA 02115; bDepartment of Biostatistics, College of Public Health and Health Professions, University of Florida, Gainesville, FL 32611; cDepartment of Epidemiology, College of Public Health and Health Professions, University of Florida, Gainesville, FL 32611; dBruno Kessler Foundation, 38123 Trento, Italy; eDondena Centre for Research on Social Dynamics and Public Policy, Universita´ Commerciale L. Bocconi, 20136 Milan, Italy; fInstitute for Scientific Interchange Foundation, 10126 Turin, Italy; gVaccine and Infectious Disease Division, Fred Hutchinson Cancer Research Center, Seattle, WA 98109; and hDepartment of Biostatistics, University of Washington, Seattle, WA 98195

Edited by Alan Hastings, University of California, Davis, CA, and approved March 30, 2017 (received for review December 8, 2016) We use a data-driven global stochastic epidemic model to ana- Using a data-driven stochastic and spatial epidemic model, we lyze the spread of the (ZIKV) in the Americas. The present numerical results providing insight into the first introduc- model has high spatial and temporal resolution and integrates tion in the region and the epidemic dynamics across the Ameri- real-world demographic, human mobility, socioeconomic, temper- cas. We use the model to analyze the spatiotemporal spread and ature, and density data. We estimate that the first intro- magnitude of the epidemic in the Americas through to February duction of ZIKV to Brazil likely occurred between August 2013 2017, accounting for seasonal environmental factors and detailed and April 2014 (90% credible interval). We provide simulated epi- population data. We also provide projections of the number of demic profiles of incident ZIKV infections for several countries in infected with ZIKV during the first trimester, along the Americas through February 2017. The ZIKV epidemic is char- with estimates for the number of cases per country acterized by slow growth and high spatial and seasonal hetero- using three different levels of risk based on empirical retrospec- geneity, attributable to the dynamics of the vector and tive studies (36, 37). to the characteristics and mobility of the human populations. We project the expected timing and number of pregnancies infected Results with ZIKV during the first trimester and provide estimates of Introduction of ZIKV to the Americas. We identify 12 major trans- microcephaly cases assuming different levels of risk as reported in portation hubs in areas related to major events held in Brazil, empirical retrospective studies. Our approach represents a mod- such as the Soccer Confederations Cup in June 2013 and the eling effort aimed at understanding the potential magnitude and Soccer World Cup in June 2014 and assumed a prior probability timing of the ZIKV epidemic and it can be potentially used as a of introduction proportional to the daily passenger flow to each template for the analysis of future mosquito-borne epidemics. hub. We then consider introduction dates between April 2013 and June 2014, including the time frame suggested by phyloge- Zika virus | computational epidemiology | metapopulation network model | netic and molecular clock analyses (.org/zika; ref. 30) vector-borne diseases through to the 2014 Soccer World Cup. Using Latin square sam- pling over the two-dimensional space (date–location), we calcu- he Zika virus (ZIKV) is an RNA virus from the lated the likelihood of replicating the observed epidemic peak Tfamily, genus (1, 2), first isolated in the in Colombia (±1 wk), as reported by Colombia’s National Insti- of in 1947 (3). It generally results in a mild disease char- tute of Health (38), and the resulting posterior density of each acterized by low-grade , , and/or , although only ∼20% of those infected are symptomatic (4). Although Significance there have been instances of sexual and perinatal/vertical trans- mission (5–12) and the potential for by transfusion is present (13), ZIKV spreads primarily through infected Mathematical and computational modeling approaches can mosquitoes (14, 15). be essential in providing quantitative scenarios of disease Until recently, ZIKV was considered a neglected tropical dis- spreading, as well as projecting the impact in the population. ease with only local outbreaks (4, 16–18). The association of Here we analyze the spatial and temporal dynamics of the ZIKV with the reported microcephaly case clusters in Brazil dur- Zika virus epidemic in the Americas with a microsimulation ing 2015 (19) led the director-general of the WHO to declare on approach informed by high-definition demographic, mobility, February 1, 2016, a Public Health Emergency of International and epidemic data. The model provides probability distribu- Concern (PHEIC) (20) that lasted for nearly 10 mo. During this tions for the time and place of introduction of Zika in Brazil, period, ZIKV spread throughout the Americas, with 47 coun- the estimate of the attack rate, timing of the epidemic in the tries and territories in the region reporting autochthonous trans- affected countries, and the projected number of newborns mission (21, 22). Many other countries with ZIKV outbreaks from women infected by Zika. These results are potentially besides Brazil have reported cases of microcephaly and other relevant in the preparation and analysis of contingency plans birth defects associated with ZIKV infection during aimed at Zika virus control. (Zika congenital syndrome) (23), and the epidemic has been under close scrutiny by all of the major public health agencies Author contributions: M.E.H., I.M.L., and A.V. designed research; Q.Z., K.S., M.C., A.P.y.P., around the world. S.M., D.M., P.P., L.R., and A.V. performed research; Q.Z., K.S., M.C., A.P.y.P., D.M., M.B., Although enhanced surveillance and new data have improved and A.V. analyzed data; and Q.Z., K.S., M.C., A.P.y.P., N.E.D., D.P.R., S.M., D.M., P.P., L.R., our understanding of ZIKV (24–29), many unknowns persist. M.B., M.E.H., I.M.L., and A.V. wrote the paper. There is uncertainty surrounding the time of introduction of the The authors declare no conflict of interest. virus to the region, although epidemiological and genetic find- This article is a PNAS Direct Submission. ings estimate that ZIKV arrived in Brazil between May and December 2013 (nextstrain.org/zika; ref. 30). Furthermore, Freely available online through the PNAS open access option. although mathematical and computational models have tackled See Commentary on page 5558. the characterization of the transmissibility and potential burden 1To whom correspondence should be addressed. Email: [email protected]. of ZIKV (31–35), little is known about the global spread of the This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10. virus in 2014 and 2015, before the WHO’s alert in early 2016. 1073/pnas.1620161114/-/DCSupplemental.

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POPULATION BIOPHYSICS AND SEE COMMENTARY PNAS PLUS BIOLOGY COMPUTATIONAL BIOLOGY phylogenetic and molecular clock analyses (nextstrain.org/zika; available database (www.zika-model.org). The earliest epidemic ref. 30). The most likely locations of ZIKV introduction, in is observed in Brazil, followed by Haiti, Honduras, Venezuela, descending order, are Rio de Janeiro (southeast), Brasilia (cen- and Colombia. The model indicates that the epidemics in most tral), Fortaleza (northeast), and Salvador (northeast). Although countries decline after July 2016, a finding supported by epidemi- Rio de Janeiro experiences the greatest passenger flow, the city ological surveillance in the region. The decline of the epidemic also experiences more seasonality in mosquito density, making its is mostly due to the fact that large outbreaks greatly deplete the likelihood to seed an epidemic sensitive to introduction date. The pool of susceptible individuals who can be exposed to the dis- cities located in the northeast of Brazil have lower passenger flow ease. In some countries (for instance, Puerto Rico) the seasonal compared with Rio de Janeiro but have higher mosquito density variation plays a role in the quick decline of the epidemic; how- and (DENV) transmission all year round. Brasilia, in ever, the first wave is generally the most important in terms of comparison, has little seasonality in terms of mosquito density and magnitude. Although the model projects activity in many places high traffic flow, although the area has low DENV transmission. throughout the Americas in 2017, the incidence is extremely small compared with the cumulative incidence of 2015/2016. Spatiotemporal ZIKV Spread. Stochastic realizations reproducing National infection ARs are projected to be high in Haiti, the observed peak in Colombia define the model output used Honduras, and Puerto Rico. Countries with larger populations to provide the spatiotemporal pattern of ZIKV spread in the and more heterogeneity in mosquito density and vector-borne Americas through to February 2017. In Fig. 2 we plot the sim- disease transmission, such as Mexico and Colombia, experience ulated epidemic profiles of incident ZIKV infections for several much lower infection ARs. For example, nearly half of Colom- countries in the region, and in Table 1 we report the associated bia’s population resides in areas of high altitude where sus- infection attack rates (ARs) through to February 1, 2016, when tained vector-borne ZIKV transmission is not possible. Due to the WHO declared a PHEIC, and through to February 28, 2017. the model’s fine spatial and temporal resolution, we are able In SI Appendix we report maps with the cumulative number of to observe significant variability in the ZIKV basic reproductive cases at the scale of 1 km × 1 km. The infection AR is defined as number R0 across locations, and even within the same location the ratio between the cumulative number of new infections (both at different times. These differences are driven by temperature, symptomatic and asymptomatic) during the period of consider- the vector distribution, and socioeconomic factors, among other ation and the total population of a given region. Estimates for variables (additional details are provided in Materials and Meth- additional countries in the Americas are provided in a publicly ods). In Fig. 3 we plot R0 in a number of areas at different

Fig. 2. Estimated daily number of new ZIKV infections (per 1,000 people) in eight affected countries in the Americas between January 2014 and February 2017. The bold line and shaded area refer to the estimated median number of infections and 95% CI of the model projections. Rates include asymptomatic infections. The median incidence is calculated each week from the stochastic ensemble output of the model and may not be representative of specific epidemic realizations. Thin lines represent a sample of specific realizations. Note that the scales on the y axes of the subplots vary. *Puerto Rico curves are constrained under the condition that the peak of incidence curve is after March 1, 2016, based on the surveillance reports (72).

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POPULATION BIOPHYSICS AND SEE COMMENTARY PNAS PLUS BIOLOGY COMPUTATIONAL BIOLOGY Fig. 4. Estimated daily number of births between October 2014 and December 2017 from women infected with ZIKV during the first trimester of pregnancy in eight affected coun- tries in the Americas. The bold line and shaded area refer to the estimated median number of births and 95% CI of the model projections, respectively. Note that Brazil is plotted on a dif- ferent scale. The median curve is calculated each week from the stochastic ensemble output of the model and may not be representative of spe- cific epidemic realizations. Thin lines represent a sample of specific realizations.

CI [26 to 36%]) in Bahia through February 2016, as determined infection AR as soon as the country extends to north and south of by our model, the estimated first trimester microcephaly risks the equator and we look at specific geographical areas where only are 2.19% (95% CI [1.98 to 2.41%]), assuming 100% overreport- A. albopictus are present. ing of microcephaly cases, and 4.52% (95% CI [4.10 to 4.96%]), assuming no overreporting. These estimates do not account Model Validation. Our results have been validated comparing our for miscarriages or other complications that may occur during projections with surveillance data that were not directly used pregnancy. to calibrate the model: the number of ZIKV infections by states In Table 1 we report the projected cumulative number of in Colombia, the weekly counts of microcephaly cases reported microcephaly cases up to February 1, 2016, and December 10, in Brazil, and the number of importations of ZIKV infections in 2017. By the time the WHO declared a PHEIC, Brazil was the continental United States (USA), as shown in Fig. 5. In Fig. the only country with a substantial (>100) number of ZIKV- 5A we compare model-based projections of the number of ZIKV attributable microcephaly cases, with cases expected to appear infections for states in Colombia with observed surveillance through July 2017. For Colombia, the model projects a consider- data through October 1, 2016 (38). As expected for a typically able number of new microcephaly cases until March–April 2017. asymptomatic or mild disease, the model projects a much larger In Venezuela, the peak in microcephaly cases was projected to number of infections than that captured by surveillance, suggest- start in September/October 2016, continuing through February ing a reporting and detection rate of 1.02% ± 0.93% (from lin- 2017. In Puerto Rico, microcephaly cases were expected to occur ear regression analysis). However, the observed data and model mostly from December 2016 to April 2017. It is important to estimates are well-correlated (Pearson’s r = 0.68, P < 0.0001), remark, however, that the microcephaly incidence tail extends replicating the often several-orders-of-magnitude difference in for most of the countries up to July/August 2017. Along with the infection burden across states within the same country. microcephaly risk, other birth defects and pregnancy complica- In Fig. 5B we compare observed data on weekly counts of tions are associated with ZIKV infection during pregnancy (36, microcephaly cases reported in Brazil through April 30, 2016 37, 39). Although we do not explicitly tabulate here specific pro- (40) with estimates from the model for each projected level of jections, they can be calculated from our model by applying the microcephaly risk given first-trimester ZIKV infection. The three estimated risk for any other to our daily number of model projection curves vary in magnitude but replicate peaks births from women infected with ZIKV. consistent with the observed data. Because the fraction of cases confirmed in Brazil is relatively low, it is not possible to identify Sensitivity to Mosquito Vector. Simulations reported here con- the most likely level of risk, although the figure suggests that the sider both and as competent ZIKV risk might exceed the lowest estimate of 0.95% (36). vectors, although less is known about the vectorial capacity of Because the computational approach explicitly simulates A. albopictus. A sensitivity analysis considering A. aegypti as the the number of daily airline passengers traveling globally, the only competent vector is provided in SI Appendix with all figures microsimulations allow us to track ZIKV infections imported and tables replicated for this scenario. Overall, results are simi- into countries with no autochthonous transmission. In Fig. 5C lar because transmission due to A. aegypti increases to compen- we plot the number of importations into states in the USA sate for the absence of the other vector. Differences in the infec- through October 5, 2016, as reported by the CDC (41) and com- tion ARs, however, are observed in areas where A. albopictus pare these results with model projections. Because the detec- is the most common or the only vector. For example, the infec- tion rate of ZIKV infections is very low, there are significantly tion AR in Brazil up to February 28, 2017, decreases from 18% fewer reported cases than projected; we estimate through a lin- (95% CI [16 to 19%]) to 16% (95% CI [14 to 17%]) if we con- ear regression fit that 5.74% ± 1.46% of both symptomatic and sider only A. aegypti. During the same time period, the infec- asymptomatic imported infections are detected. Nonetheless, tion AR in Mexico decreases from 5% (95% CI [4 to 6%]) to model projections are highly correlated with the observed data 4% (95% CI [2 to 5%]). A more thorough analysis of the differ- (Pearson’s r = 0.93, P < 0.0001), as shown in Fig. 5C, Inset. A ences between the two scenarios is reported in SI Appendix. At further validation of the model is provided by the reported num- the country scale, in Brazil and other key countries those differ- ber of ZIKV cases of pregnant women in the USA. A high ences seem small because A. aegypti and A. albopictus have very detection rate is expected in this closely monitored population. similar presence. However, we see noticeable differences in the As of September 29, 2016, 837 pregnant women in the USA

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POPULATION BIOPHYSICS AND SEE COMMENTARY PNAS PLUS BIOLOGY COMPUTATIONAL BIOLOGY first wave was not recognized as ZIKV until early 2016. The sec- term ZIKV transmission is crucial to plan for future Zika control ond wave, between January and May 2016, affected mostly south- activities and for finding sites for phase-III Zika trials. ern states in Brazil (46). This progression of the epidemic is in This is a topic for future research. agreement with the reconstruction of the movement of ZIKV in Another prominent feature emerging from the numerical Brazil using confirmed cases at the municipal level (33). results is the extreme heterogeneity in the infection ARs across The virus also circulated early on in the Caribbean, with ZIKV countries. We find more than a sevenfold difference between samples isolated in Haiti at the end of 2014, and a possible Honduras and Mexico, exhibiting infection ARs of 35% (95% first peak occurred in October 2015 (47). Colombia first isolated CI [30 to 39%]) and 5% (95% CI [4 to 6%]), respectively. These ZIKV in October 2015, at which time it spread rapidly from the large differences in infection ARs, which are also observable at Caribbean coast to cities infested with A. aegypti (48). The model finer geographical resolutions, stem from variation in climatic suggests an introduction to Colombia as early as March–April factors, mosquito densities, and socioeconomic factors. 2015, potentially overlapping with the Easter holiday, which is We project the numbers of births from women who were a period of high mobility within and between countries in the infected with ZIKV during the first trimester of their pregnancy. region. ZIKV transmission in Venezuela follows a similar trajec- There is a well-defined time lag between the epidemic curve and tory, first isolated in November 2015 and present in all states by this birth curve. Brazil, which likely experienced its first ZIKV July 2016 (49). Since March 2016, reported cases have declined epidemic peak in March 2015, had a sharp rise in microcephaly in both countries, consistent with our model estimates. cases in September 2015, consistent with what was observed in Our model estimates ZIKV transmission in El Salvador and the field (40). In Colombia 132 confirmed cases of congenital Honduras increasing around July 2015. ZIKV was first detected Zika syndrome had been observed as of March 11, 2017 (56). in El Salvador in November 2015 and in Honduras in December However, at the same date, 538 additional cases are under study, 2015 (50, 51). Although the first ZIKV infection was confirmed in thus not yet allowing a risk factor estimate from the model. Puerto Rico in the last week of December 2015 (52), the model Note that the projected number of microcephaly cases estimated estimates ZIKV transmission in Puerto Rico beginning around by the model varies considerably depending on the assumed August 2015. In Mexico, the first infection was reported to the first-trimester risk, for which only retrospective estimates are surveillance system at the end of November 2015 (53), although available (36, 37). We also note that with as many as 80% of circulation may have begun in September 2015. ZIKV infections being asymptomatic (4, 39), most of ZIKV- The epidemic has moved slowly and is mostly constrained by infected pregnant women giving birth may not have experienced seasonality in ZIKV transmissibility. Seasonal drivers and time symptoms during pregnancy. Thus, clinicians should be cautious of introduction result in multiple waves (54) across several coun- before ruling out ZIKV as the cause of birth defects. The results tries, as projected for Brazil, Honduras, and Mexico. To show the presented here, however, could be used as a baseline to uncover importance of the seasonal drivers in shaping the epidemic, we possible disagreement with the observed data and highlight the report in SI Appendix the analysis of two counterfactual scenar- need for additional key evidence to enhance our understanding ios in which we eliminate the differences in the seasonal drivers of the link between ZIKV and birth defects (57). across the region. This analysis clearly shows that ignoring the Available data on the ZIKV epidemic suffer from several spatial variation of seasonal drivers gives rise to unrealistic pat- limitations. Although the disease has likely been spreading in terns incompatible with the observed data. the Americas since late 2013, infection detection and report- Another relevant result of the model is that incidence rates ing began much later and likely increased after the WHO’s dramatically decrease in all considered countries by the end declaration of a PHEIC in February 2016. Case reporting is of 2016. The drop in incidence in the model is largely due to inconsistent across countries. Furthermore, comparatively few the epidemic’s depleting the susceptible pool. This implies that infections are laboratory-confirmed; this presents an additional ZIKV epidemics could settle into the typical seasonal pattern challenge because symptomatic cases with other etiologies of mosquito-borne diseases such as DENV. Transmission may may be misdiagnosed, and asymptomatic infections are almost be low for several years with a gradual buildup in susceptibil- entirely missed. Once a reliable ZIKV test is avail- ity due to births (55). In the real world, however, other factors able, seroprevalence studies can help determine the full extent of such as vector control and/or specific local weather conditions these outbreaks. For external validation, we compare modeling could have contributed to the drop of incidence along with herd results with data from Brazil, Colombia, and the USA that were immunity. Because these factors might change in the future, sub- not used to calibrate the model. We are able to replicate rel- sequent epidemic waves may occur. Precise projection of long- ative trends, although we estimate significantly higher absolute

Fig. 6. Schematic representation of the integration of data layers and the computational flow chart defining the GLEAM model for ZIKV.

E4340 | www.pnas.org/cgi/doi/10.1073/pnas.1620161114 Zhang et al. Downloaded by guest on September 30, 2021 Downloaded by guest on September 30, 2021 ihrslto eorpi,hmnmblt,scocnmc(gecon.yale. socioeconomic edu mobility, integrates human model individual- This demographic, described (60–65). high-resolution model previously epidemic spatial a and (GLEAM), stochastic, based, Model Mobility and Epidemic Summary. Model Methods and Materials generalized computa- . be and a potentially provides can also other that to here framework presented modeling vaccine study ZIKV tional out- epi- phase-III The local of the sites. and planning international the of trial for for planning timing and in response, and aid break as magnitude well the as and demic, data for surveillance observed results indications of numerical provide interpretation the the in from help the emerging may to inherent framework limitations the and assumptions approach, the of light in tiously i a efre,IBapoa a o eurd eew expanded we Here required. not was approval IRB performed, was sis research/analy- subject human no because Global2011/GlobalTsT2011.html); temporal the as well by as mobility: human character- characterized and AR population-level istics, weather, epidemic local infection from the model resulting the The pattern of ZIKV. in dynamic of spread frame- heterogeneity slow global methodological the the of a captures analysis provides the here for work presented model The Conclusions model. the of calibration These the from refine available awareness. to becomes regions increased information ZIKV-affected more to as due change popula- may changes vector results the behavioral not control or do to we tion fea- interventions Finally, socioeconomic health included. not public specific also model are The travelers 59). airline of number (9–12, the tures reproductive incidence where small low areas a and in has trans- relevance the transmission acquire of mosquito-borne component might sexual not however, are The mission, transmission model. of the modes other in litera- and incorporated the Sexual in 58). detailed 34, as (32, limitations ture have but data published available accurate from are maps to more presence/absence needed Mosquito and calibrations. is estimates local research parameter further ZIKV-specific (38); observed provide Health the of and Institute Polynesia National (± cal- French Colombia been in from peak has data epidemic model data using The more needed. by certainly plausible, ibrated are is ZIKV for assumption to expressions this specific some Although on modeled of data. are DENV use that transmissibility the of dependence includes modeled temperature is This mosquito- transmission diseases. other and result, borne DENV to a the similarly behaves As con- to ZIKV data. it assuming due and available unavoidable epidemic, of approximations ZIKV sparsity the and of assumptions assessment tains rapid a for need country. the on depending from 6% ranging about rates to detection 1% and reporting suggesting numbers, hn tal. et Zhang • • • • lhuhtemdln eut hudb nepee cau- interpreted be should results modeling the Although h oeigapoc rsne eei oiae ythe by motivated is here presented approach modeling The in ol ecekdaantosre aai h future. the in data projec- observed These against risk. cases checked be of microcephaly could of levels tions of newborns different trimester assuming number first of 2017 potential the through number during the ZIKV the and by pregnancy of infected estimation USA women from the allows into model cases The travel-related esti- explicit of countries. other the number and allows the data of travel mation airline of and integration ARs countries. The infection affected ZIKV the in for timing estimates epidemic provides 2017. it February through particular, spatiotem- Americas In the the in ZIKV of of estimates spread poral allow epidemic. the simulations of numerical dynamics The and past compre- a the time generating of the Brazil, picture in hensive for ZIKV distribution of introduction probability of place a yields model The ,adtmeauedt (climate.geog.udel.edu/∼climate/html data temperature and ), tasitdvco-on iess uha dengue as such diseases, vector-borne Aedes-transmitted osuysaitmoa IVsra,w s h Global the use we spread, ZIKV spatiotemporal study To k,a eotdb Colombia’s by reported as wk), 1 pages/ lt h ies fitrs.Temdlue nidvda dynamic individual an the through uses interact chain Subpopulations model by processes. defined The multinomial mathematically and are interest. binomial transitions stochastic of discrete, disease where different the 230 ulate roughly in subpopulations year). areas. by 3,200 vary urban (numbers over different countries includes in hubs model transportation The major sur- Earth’s around the of centered tessellation face Voronoi-like a by defined subpopulations into Cen- consid- 25-km Application model 0 of and The cells (sedac.ciesin.columbia.edu). Data geographical ers University Socioeconomic dis- Columbia the Population obtained at from infectious Gridded information ter project the of population World of spread the uses database spatial of population GLEAM high-resolution the level. the global of from data the simulations real-world at uses silico that eases in platform modeling perform Diseases. epidemic to Vector-Borne stochastic of fully Spread a is the for Model Global DENV. and ZIKV ZIKV available between the similarities on pop- assumed mosquito and based literature and ranges human parameter the plausible compart- in assigning a stages 66). ulations, use disease we (32, the (18), of exposure classification approaches of mental modeling risk previous population to and Similar factors socioeconomic on between data incorporate to aaeescnb on nrf.2 ,1,5,ad68–70. and 55, 18, 4, the 2, for refs. in values found Specific be can geolocation-dependent. parameters and temperature- model. are the of that temperature-dependent. parameters are is the that vector of mosquito parameters Summary the for (B) are below. model individuals compartmental to shown where The virus; disease removed, infectious. the the longer or transmit transmit no recovered to can and and yet mosquitoes; infected able susceptible are not individuals are where but infectious, infected exposed, acquire mosquitoes; can are infectious which individuals with susceptible, where (bites) compartments: contacts through top infection four the the of one occupy 7. Fig. B A ihnec upplto,acmatetlmdli sdt sim- to used is model compartmental a subpopulation, each Within × 5k qaefrclsaogErhseutr LA ruscells groups GLEAM equator. Earth’s along cells for square 25-km oprmna lsicto o IVifcin uascan Humans infection. ZIKV for classification Compartmental (A) Aedes .25 PNAS ◦ × oqiodniy(8 n h association the and (58) density mosquito 0.25 | ulse nieArl2,2017 25, April online Published ◦ orsodn oa approximately an to corresponding , ,G T, dep eoe parameters denotes h LA model GLEAM The T dep denotes | E4341

POPULATION BIOPHYSICS AND SEE COMMENTARY PNAS PLUS BIOLOGY COMPUTATIONAL BIOLOGY mechanistically simulated mobility and commuting patterns of disease car- can calculate the posterior probabilities of interest. The sensitivity analysis riers. Mobility includes global air travel (www.oag.com), and GLEAM sim- for the others scenarios considers an additional 200,000 simulations in total. ulates the number of passengers traveling daily worldwide using available data on origin–destination flows among indexed subpopulations. ZIKV Transmission Dynamics. Fig. 7A describes the compartmental classifi- The transmissibility of vector-borne diseases is associated with strong spa- cations used to simulate ZIKV transmission dynamics. Humans can occupy tial heterogeneity, driven by variability and seasonality in vector abundance, one of four compartments: susceptible individuals SH who lack immunity the temperature dependence modulating the vector competence, and the against the infection, exposed individuals EH who have acquired the infec- characteristics of the exposed populations. Many locations, such as those at tion but are not yet infectious, infected individuals IH who can transmit high elevation, are not at risk for autochthonous ZIKV transmission simply the infection (and may or may not display symptoms), and removed indi- because the vector is absent. In other locations the vector may be present viduals RH who no longer have the infection and are immune to further but sustained transmission is not possible because of environmental factors ZIKV infection. We consider the human population size to be constant, that that affect the vector’s population dynamics, such as temperature or pre- is, SH + EH + IH + RH = NH. The mosquito vector population is described by cipitation. Housing conditions, availability of air conditioning, and socio- the number of susceptible SV , exposed EV , and infectious mosquitoes IV . The economic factors also contribute significantly to determining the fraction transmission model is fully stochastic. Transitions across compartments, the of the population likely exposed to the vector. To extend the GLEAM model human-to-mosquito force of infection, and the mosquito-to-human force to simulate vector-borne diseases, a number of new datasets with high spa- of infection are described by parameters that take into account the specific tial resolution are integrated, including the following: abundance of mosquitoes and temperature dependence at the cell level. • Global terrestrial air temperature data: The global air temper- Exposed individuals become infectious at a rate H, which is inversely pro- ature dataset (climate.geog.udel.edu/∼climate/html pages/Global2011/ portional to the mean intrinsic latent period of the infection (68). These GlobalTsT2011.html) contains monthly mean temperatures at a spatial infectious individuals then recover from the disease at a rate µH (18), which resolution of 0.5◦ × 0.5◦. To match the spatial resolution of GLEAM’s is inversely proportional to the mean infectious period. The mosquito-to- gridded population density map, the temperature for each population human force of infection follows the usual mass-action law and is the prod- cell is extracted from the nearest available point in the temperature uct of the number of mosquitoes per person, the daily mosquito biting rate, dataset. Daily average temperatures are linearly interpolated from each and specific ZIKV infection transmissibility per day, the mosquito-to-human V population’s monthly averages. probability of transmission (69), and the number I of infected mosquitoes. • Global A. aegypti and A. albopictus distribution: The global A. aegypti Exposed mosquitoes transition to the infectious class at a rate V , which is and A. albopictus distribution database provides uncertainty estimates inversely proportional to the mean extrinsic latent period in the mosquito for the vector’s distribution at a spatial resolution of 5 km × 5 km (58). population (2). Susceptible, exposed, and infectious mosquitoes all die at a • Geolocalized economic data: The geophysically scaled economic dataset rate that is inversely proportional to the mosquito lifespan, µV (70). The (G-Econ), developed by Nordhaus et al. (67), maps the per capita Gross mosquito-to-human force of infection follows the usual mass-action law Domestic Product [GDP, computed at purchasing power parity (PPP) in each subpopulation whose linear extension varies from a few miles to exchange rates] at a 1◦ × 1◦ resolution. To estimate the per capita gross about 50 miles depending on the population density and specific area of cell product at PPP rates, the amount is distributed across GLEAM cells the world. A full description of the stochastic model and the equations is proportionally to each cell’s population size. The data have also been provided in SI Appendix. rescaled to reflect 2015 GDP per capita (PPP) estimates. A summary of the parameters defining the disease dynamics is reported in Fig. 7B. The empirical evidence related to the ZIKV infection in both These databases are combined to model the key drivers of ZIKV trans- human and mosquito populations is fairly limited at the moment. We have mission, as illustrated in combination with necessary parameters in Fig. performed a review of the current studies of ZIKV and collected plausible 6. Temperature affects many important disease parameters, including the ranges for these parameters. As in other studies, we have assumed that the time- and cell-specific values of R , whose variation induces seasonality 0 drivers of ZIKV transmission are analogous to those of DENV. In particular, and spatial heterogeneity in the model. Temperature data are also used we have considered that mosquito lifespan, mosquito abundance, and the together with the mosquito presence distribution data to define the daily transmission probability per bite depend on the temperature level. mosquito abundance (number of mosquitoes per human) in each cell, as detailed in SI Appendix, section 2. Data on mosquito abundance and tem- perature are used to identify cells where ZIKV outbreaks are not possi- Model Calibration. The calibration of the disease dynamic model is per- ble because of environmental factors. The human populations in these formed by a Markov chain Monte Carlo analysis of data reported from cells are thus considered unexposed to ZIKV and susceptible individuals are the 2013 ZIKV epidemic in (18). Setting the extrinsic and intrinsic latent periods and the human infectious period to reference val- assigned an environmental rescaling factor, ren, as described SI Appendix, section 3. Finally, we use historical data and G-Econ to provide a socio- ues and using average daily temperatures of French Polynesia, we estimate a basic reproduction number at the temperature T = 25◦C for French Poly- economic rescaling factor, rse, reflecting how exposure to the vector is nesia FP = 2.75 (95% CI [2.53 to 2.98]), which is consistent with other ZIKV impacted by socioeconomic variables such as availability of air condition- R0 outbreak analyses (18, 31). Because the reproduction number depends on ing. The derivation of these rescaling factors is provided in SI Appendix, section 3. the disease serial interval, we report a sensitivity analysis in SI Appendix con- Once the data layers and parameters have been defined, the model sidering the upper and lower extremes of plausible serial intervals. Briefly, the estimated FP values are 2.06 (95% CI [1.91 to 2.22]) and 3.31 (95% runs using discrete time steps of one full day to simulate the transmission R0 dynamic model (described in detail below), incorporating human mobil- CI [3.03 to 3.6]) for the shortest and longest serial intervals, respectively. ity between subpopulations, and partially aggregating the results at the The R0 values are in the range of those estimated from local outbreaks in = . = . desired level of geographic resolution. The model is fully stochastic and from San Andres Island (R0 1 41) and Girardot, Colombia (R0 4 61) (71); how- any nominally identical initialization (initial conditions and disease model) ever, it is worth recalling that the reproductive number depends on the generates an ensemble of possible epidemics, as described by newly gener- location and on time through seasonal temperature changes. The calibra- ated infections, time of arrival of the infection in each subpopulation, and tion in French Polynesia provides the basic transmissibility of ZIKV. However, the number of traveling carriers. The Latin square sampling of the initial variations in temperature and mosquito abundance yield varying R0 in each introduction of ZIKV in Latin America and the ensuing statistical analysis is subpopulation tracked by the model as discussed in SI Appendix. performed on 150,000 stochastic epidemic realizations. From those realiza- ACKNOWLEDGMENTS. This work was supported by Models of Infec- tions we find the probability p(x) and p(x|θ), defined as the probability of tious Disease Agent Study, National Institute of General Medical Sciences the evidence (the epidemic peak in Colombia as from surveillance data) and Grant U54GM111274, European Commission Horizon 2020 CIMPLEX Grant the likelihood of the evidence given the parameters θ specifying the date 641191, and a Colombian Department of Science and Technology Fulbright- and location of introduction of ZIKV in Brazil. From those distributions we Colciencias scholarship (to D.P.R.).

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POPULATION BIOPHYSICS AND SEE COMMENTARY PNAS PLUS BIOLOGY COMPUTATIONAL BIOLOGY