Spread of Zika virus in the Americas

Abstract

Significance
Mathematical and computational modeling approaches can be essential in providing quantitative scenarios of disease spreading, as well as projecting the impact in the population. Here we analyze the spatial and temporal dynamics of the Zika virus epidemic in the Americas with a microsimulation approach informed by high-definition demographic, mobility, and epidemic data. The model provides probability distributions for the time and place of introduction of Zika in Brazil, the estimate of the attack rate, timing of the epidemic in the affected countries, and the projected number of newborns from women infected by Zika. These results are potentially relevant in the preparation and analysis of contingency plans aimed at Zika virus control.

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BIOPHYSICS AND
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Spread of Zika virus 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, Universit´
a 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-
lyze the spread of the Zika virus (ZIKV) in the Americas. The
model has high spatial and temporal resolution and integrates
real-world demographic, human mobility, socioeconomic, temper-
ature, and vector density data. We estimate that the first intro-
duction of ZIKV to Brazil likely occurred between August 2013
and April 2014 (90% credible interval). We provide simulated epi-
demic profiles of incident ZIKV infections for several countries in
the Americas through February 2017. The ZIKV epidemic is char-
acterized by slow growth and high spatial and seasonal hetero-
geneity, attributable to the dynamics of the mosquito vector and
to the characteristics and mobility of the human populations. We
project the expected timing and number of pregnancies infected
with ZIKV during the first trimester and provide estimates of
microcephaly cases assuming different levels of risk as reported in
empirical retrospective studies. Our approach represents a mod-
eling effort aimed at understanding the potential magnitude and
timing of the ZIKV epidemic and it can be potentially used as a
template for the analysis of future mosquito-borne epidemics.
Zika virus |computational epidemiology |metapopulation network model |
vector-borne diseases
The Zika virus (ZIKV) is an RNA virus from the Flaviviridae
family, genus Flavivirus (1, 2), first isolated in the Zika Forest
of Uganda in 1947 (3). It generally results in a mild disease char-
acterized by low-grade fever, rash, and/or conjunctivitis, although
only ∼20% of those infected are symptomatic (4). Although
there have been instances of sexual and perinatal/vertical trans-
mission (5–12) and the potential for transmission by transfusion
is present (13), ZIKV spreads primarily through infected Aedes
mosquitoes (14, 15).
Until recently, ZIKV was considered a neglected tropical dis-
ease with only local outbreaks (4, 16–18). The association of
ZIKV with the reported microcephaly case clusters in Brazil dur-
ing 2015 (19) led the director-general of the WHO to declare on
February 1, 2016, a Public Health Emergency of International
Concern (PHEIC) (20) that lasted for nearly 10 mo. During this
period, ZIKV spread throughout the Americas, with 47 coun-
tries and territories in the region reporting autochthonous trans-
mission (21, 22). Many other countries with ZIKV outbreaks
besides Brazil have reported cases of microcephaly and other
birth defects associated with ZIKV infection during pregnancy
(Zika congenital syndrome) (23), and the epidemic has been
under close scrutiny by all of the major public health agencies
around the world.
Although enhanced surveillance and new data have improved
our understanding of ZIKV (24–29), many unknowns persist.
There is uncertainty surrounding the time of introduction of the
virus to the region, although epidemiological and genetic find-
ings estimate that ZIKV arrived in Brazil between May and
December 2013 (nextstrain.org/zika; ref. 30). Furthermore,
although mathematical and computational models have tackled
the characterization of the transmissibility and potential burden
of ZIKV (31–35), little is known about the global spread of the
virus in 2014 and 2015, before the WHO’s alert in early 2016.
Using a data-driven stochastic and spatial epidemic model, we
present numerical results providing insight into the first introduc-
tion in the region and the epidemic dynamics across the Ameri-
cas. We use the model to analyze the spatiotemporal spread and
magnitude of the epidemic in the Americas through to February
2017, accounting for seasonal environmental factors and detailed
population data. We also provide projections of the number of
pregnancies infected with ZIKV during the first trimester, along
with estimates for the number of microcephaly cases per country
using three different levels of risk based on empirical retrospec-
tive studies (36, 37).
Results
Introduction of ZIKV to the Americas. We identify 12 major trans-
portation hubs in areas related to major events held in Brazil,
such as the Soccer Confederations Cup in June 2013 and the
Soccer World Cup in June 2014 and assumed a prior probability
of introduction proportional to the daily passenger flow to each
hub. We then consider introduction dates between April 2013
and June 2014, including the time frame suggested by phyloge-
netic and molecular clock analyses (nextstrain.org/zika; ref. 30)
through to the 2014 Soccer World Cup. Using Latin square sam-
pling over the two-dimensional space (date–location), we calcu-
lated the likelihood of replicating the observed epidemic peak in
Colombia (±1 wk), as reported by Colombia’s National Institute
of Health (38), and the resulting posterior density of each loca-
tion and date combination. The Colombian epidemic was used
Significance
Mathematical and computational modeling approaches can
be essential in providing quantitative scenarios of disease
spreading, as well as projecting the impact in the population.
Here we analyze the spatial and temporal dynamics of the
Zika virus epidemic in the Americas with a microsimulation
approach informed by high-definition demographic, mobility,
and epidemic data. The model provides probability distribu-
tions for the time and place of introduction of Zika in Brazil,
the estimate of the attack rate, timing of the epidemic in the
affected countries, and the projected number of newborns
from women infected by Zika. These results are potentially
relevant in the preparation and analysis of contingency plans
aimed at Zika virus control.
Author contributions: M.E.H., I.M.L., and A.V. designed research; Q.Z., K.S., M.C., A.P.y.P.,
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.,
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.,
M.B., M.E.H., I.M.L., and A.V. wrote the paper.
The authors declare no conflict of interest.
This article is a PNAS Direct Submission.
Freely available online through the PNAS open access option.
1To whom correspondence should be addressed. Email: a.vespignani@northeastern.edu.
This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.
1073/pnas.1620161114/-/DCSupplemental.
www.pnas.org/cgi/doi/10.1073/pnas.1620161114 PNAS Early Edition |1 of 10

B
A
C
Fig. 1. Posterior distribution for ZIKV introductions in 12 major transportation hubs in Brazil between April 2013 and June 2014, incorporating the
likelihood of replicating the observed epidemic peak in Colombia. (A) Full posterior distribution as a function of location and time of introduction.
(B) Marginal posterior distribution for time (month) of introduction. (C) Marginal posterior distribution for location of introduction.
to calibrate this analysis because of the large number of cases
observed and overall consistency in reporting.
In Fig. 1Awe plot the posterior distribution as a function of
introduction date and location, and in Fig. 1 Band Cwe plot the
marginal posterior distributions of introduction date and loca-
tion separately. The largest posterior density is associated with an
introduction in Rio de Janeiro in December 2013. The 90% cred-
ible interval for the most likely date extends from August 2013 to
April 2014, with the mode in December 2013, in agreement with
phylogenetic and molecular clock analyses (nextstrain.org/zika;
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ref. 30). The most likely locations of ZIKV introduction, in
descending order, are Rio de Janeiro (southeast), Brasilia (cen-
tral), Fortaleza (northeast), and Salvador (northeast). Although
Rio de Janeiro experiences the greatest passenger flow, the city
also experiences more seasonality in mosquito density, making
its likelihood to seed an epidemic sensitive to introduction date.
The cities located in the northeast of Brazil have lower passen-
ger flow compared with Rio de Janeiro but have higher mosquito
density and dengue virus (DENV) transmission all year round.
Brasilia, in comparison, has little seasonality in terms of mosquito
density and high traffic flow, although the area has low DENV
transmission.
Spatiotemporal ZIKV Spread. Stochastic realizations reproducing
the observed peak in Colombia define the model output used
to provide the spatiotemporal pattern of ZIKV spread in the
Americas through to February 2017. In Fig. 2 we plot the sim-
ulated epidemic profiles of incident ZIKV infections for several
countries in the region, and in Table 1 we report the associated
infection attack rates (ARs) through to February 1, 2016, when
the WHO declared a PHEIC, and through to February 28, 2017.
In SI Appendix we report maps with the cumulative number of
cases at the scale of 1 km ×1 km. The infection AR is defined as
the ratio between the cumulative number of new infections (both
symptomatic and asymptomatic) during the period of consider-
ation and the total population of a given region. Estimates for
additional countries in the Americas are provided in a publicly
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 yaxes 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).
available database (www.zika-model.org). The earliest epidemic
is observed in Brazil, followed by Haiti, Honduras, Venezuela,
and Colombia. The model indicates that the epidemics in most
countries decline after July 2016, a finding supported by epidemi-
ological surveillance in the region. The decline of the epidemic
is mostly due to the fact that large outbreaks greatly deplete the
pool of susceptible individuals who can be exposed to the dis-
ease. In some countries (for instance, Puerto Rico) the seasonal
variation plays a role in the quick decline of the epidemic; how-
ever, the first wave is generally the most important in terms of
magnitude. Although the model projects activity in many places
throughout the Americas in 2017, the incidence is extremely
small compared with the cumulative incidence of 2015/2016.
National infection ARs are projected to be high in Haiti,
Honduras, and Puerto Rico. Countries with larger populations
and more heterogeneity in mosquito density and vector-borne
disease transmission, such as Mexico and Colombia, experience
much lower infection ARs. For example, nearly half of Colom-
bia’s population resides in areas of high altitude where sus-
tained vector-borne ZIKV transmission is not possible. Due to
the model’s fine spatial and temporal resolution, we are able
to observe significant variability in the ZIKV basic reproductive
number R0across locations, and even within the same location
at different times. These differences are driven by temperature,
the vector distribution, and socioeconomic factors, among other
variables (additional details are provided in Materials and Meth-
ods). In Fig. 3 we plot R0in a number of areas at different
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Table 1. Projected ZIKV infection ARs through the time of the WHO declaration of a PHEIC on February 1, 2016, and through February
28, 2017, in eight affected countries in the Americas
Infection AR % Cumulative microcephaly cases (median with 95% CI)
(median with 95% CI) First-trimester risk: 0.95% First-trimester risk: 2.19% First-trimester risk: 4.52%
Feb. 1, 2016 Feb. 28, 2017 Feb. 1, 2016 Dec. 10, 2017 Feb. 1, 2016 Dec. 10, 2017 Feb. 1, 2016 Dec. 10, 2017
Brazil 16 [13 to 18] 18 [16 to 19] 839 [138 to 1,140] 1,297 [1,190 to 1,428] 1,934 [318 to 2,628] 2,991 [2,744 to 3,291] 3,992 [656 to 5,424] 6,173 [5,664 to 6,792]
Colombia 4 [3 to 7] 12 [11 to 14] 0 [0 to 4] 219 [194 to 248] 0 [0 to 10] 504 [447 to 572] 1 [0 to 20] 1,041 [922 to 1,180]
Mexico 1 [0 to 2] 5 [4 to 6] 0 [0 to 2] 314 [226 to 367] 0 [0 to 5] 723 [522 to 845] 1 [0 to 11] 1,493 [1,077 to 1,744]
Puerto Rico* 2 [0 to 7] 20 [13 to 28] 0 [0 to 0] 19 [13 to 26] 0 [0 to 0] 43 [29 to 60] 0 [0 to 0] 88 [60 to 124]
El Salvador 1 [0 to 13] 16 [13 to 18] 0 [0 to 0] 39 [32 to 47] 0 [0 to 0] 91 [75 to 108] 0 [0 to 1] 187 [154 to 223]
Honduras 8 [0 to 28] 35 [30 to 39] 0 [0 to 1] 144 [124 to 163] 0 [0 to 3] 332 [286 to 376] 0 [0 to 7] 686 [590 to 775]
Haiti 43 [1 to 54] 49 [43 to 55] 0 [0 to 54] 316 [276 to 357] 0 [0 to 124] 728 [637 to 824] 0 [0 to 256] 1,502 [1,315 to 1,700]
Venezuela 13 [5 to 19] 19 [16 to 21] 2 [0 to 96] 271 [237 to 308] 5 [0 to 221] 624 [546 to 711] 9 [0 to 456] 1,288 [1,127 to 1,468]
Median estimates and 95% CIs are provided. ZIKV ARs include asymptomatic infections. The denominator is the entire population of the country, including regions not exposed to the vector.
Cumulative microcephaly cases due to ZIKV infection during the first trimester of pregnancy through the time of the WHO declaration of a PHEIC on February 1, 2016, and through December 10,
2017, in eight affected countries in the Americas. We consider three different risks of microcephaly associated with ZIKV infection during the first trimester: 0.95% first-trimester risk based on a study
of the 2013–2014 French Polynesian outbreak (36) and 2.19% (100% overreporting) and 4.52% (no overreporting) first-trimester risks, based on a study of Bahia, Brazil (37), given a model-estimated
31%infection AR in Bahia.
*Puerto Rico curves constrained under the condition that the peak of ZIKV incidence curve is after March 1, 2016, based on surveillance data (72).
times throughout the year. Equatorial regions experience less
seasonality than nonequatorial regions, where changes in tem-
perature have a strong impact on the mosquito population, and
thus R0. Large areas with unexposed populations are visible,
such as in high-altitude regions of Colombia. It is also worth
remarking that maximum R0is not the sole determinant of the
epidemic magnitude, because seasonality patterns and a small
fraction of exposed individuals may not allow large outbreaks to
occur.
Projected ZIKV Infections in Childbearing Women and Microcephaly
Cases. Using the epidemic profiles generated by the model
we project the number of ZIKV infections in childbearing
women following the model proposed in the study of ZIKV–
microcephaly association for the 2013–2014 French Polynesia
Fig. 3. Monthly seasonality for the time- and
location-dependent basic reproductive number, R0.
The equatorial regions display less seasonality than
the nonequatorial regions, where the changes of
the season have a strong impact on the temper-
ature and consequently on the basic reproductive
number, R0.
outbreak (36). In Fig. 4 we plot the daily number of births
through December 2017 from women infected with ZIKV dur-
ing their first trimester of pregnancy in several countries. Indeed,
the first trimester of pregnancy is when the risk of microcephaly
is the highest (36, 37, 39). The curves closely resemble the epi-
demic profiles in Fig. 2 but shifted forward in time by about
40 wk. We construct our estimates using country-specific birth
rates, as detailed in SI Appendix, section 4.
To estimate the number of microcephaly cases we adopt three
different probabilities, as reported in two empirical retrospec-
tives studies (36, 37). The first estimate of microcephaly risk for
ZIKV infected pregnancies is 0.95% (95% confidence interval
(CI) [0.34 to 1.91%]), from a study in French Polynesia (36). The
remaining two estimates come from a study performed in Bahia,
Brazil (37). Given an overall ZIKV infection AR of 31% (95%
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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
by our model, the estimated first trimester microcephaly risks
are 2.19% (95% CI [1.98 to 2.41%]), assuming 100% overreport-
ing of microcephaly cases, and 4.52% (95% CI [4.10 to 4.96%]),
assuming no overreporting. These estimates do not account
for miscarriages or other complications that may occur during
pregnancy.
In Table 1 we report the projected cumulative number of
microcephaly cases up to February 1, 2016, and December 10,
2017. By the time the WHO declared a PHEIC, Brazil was
the only country with a substantial (>100) number of ZIKV-
attributable microcephaly cases, with cases expected to appear
through July 2017. For Colombia, the model projects a consider-
able number of new microcephaly cases until March–April 2017.
In Venezuela, the peak in microcephaly cases was projected to
start in September/October 2016, continuing through February
2017. In Puerto Rico, microcephaly cases were expected to occur
mostly from December 2016 to April 2017. It is important to
remark, however, that the microcephaly incidence tail extends
for most of the countries up to July/August 2017. Along with the
microcephaly risk, other birth defects and pregnancy complica-
tions are associated with ZIKV infection during pregnancy (36,
37, 39). Although we do not explicitly tabulate here specific pro-
jections, they can be calculated from our model by applying the
estimated risk for any other complication to our daily number of
births from women infected with ZIKV.
Sensitivity to Mosquito Vector. Simulations reported here con-
sider both Aedes aegypti and Aedes albopictus as competent ZIKV
vectors, although less is known about the vectorial capacity of
A. albopictus. A sensitivity analysis considering A. aegypti as the
only competent vector is provided in SI Appendix with all figures
and tables replicated for this scenario. Overall, results are simi-
lar because transmission due to A. aegypti increases to compen-
sate for the absence of the other vector. Differences in the infec-
tion ARs, however, are observed in areas where A. albopictus
is the most common or the only vector. For example, the infec-
tion AR in Brazil up to February 28, 2017, decreases from 18%
(95% CI [16 to 19%]) to 16% (95% CI [14 to 17%]) if we con-
sider only A. aegypti. During the same time period, the infec-
tion AR in Mexico decreases from 5% (95% CI [4 to 6%]) to
4% (95% CI [2 to 5%]). A more thorough analysis of the differ-
ences between the two scenarios is reported in SI Appendix. At
the country scale, in Brazil and other key countries those differ-
ences seem small because A. aegypti and A. albopictus have very
similar presence. However, we see noticeable differences in the
infection AR as soon as the country extends to north and south of
the equator and we look at specific geographical areas where only
A. albopictus are present.
Model Validation. Our results have been validated comparing our
projections with surveillance data that were not directly used
to calibrate the model: the number of ZIKV infections by states
in Colombia, the weekly counts of microcephaly cases reported
in Brazil, and the number of importations of ZIKV infections in
the continental United States (USA), as shown in Fig. 5. In Fig.
5Awe compare model-based projections of the number of ZIKV
infections for states in Colombia with observed surveillance
data through October 1, 2016 (38). As expected for a typically
asymptomatic or mild disease, the model projects a much larger
number of infections than that captured by surveillance, suggest-
ing a reporting and detection rate of 1.02% ±0.93% (from lin-
ear regression analysis). However, the observed data and model
estimates are well-correlated (Pearson’s r= 0.68,P<0.0001),
replicating the often several-orders-of-magnitude difference in
infection burden across states within the same country.
In Fig. 5Bwe compare observed data on weekly counts of
microcephaly cases reported in Brazil through April 30, 2016
(40) with estimates from the model for each projected level of
microcephaly risk given first-trimester ZIKV infection. The three
model projection curves vary in magnitude but replicate peaks
consistent with the observed data. Because the fraction of cases
confirmed in Brazil is relatively low, it is not possible to identify
the most likely level of risk, although the figure suggests that the
risk might exceed the lowest estimate of 0.95% (36).
Because the computational approach explicitly simulates
the number of daily airline passengers traveling globally, the
microsimulations allow us to track ZIKV infections imported
into countries with no autochthonous transmission. In Fig. 5C
we plot the number of importations into states in the USA
through October 5, 2016, as reported by the CDC (41) and com-
pare these results with model projections. Because the detec-
tion rate of ZIKV infections is very low, there are significantly
fewer reported cases than projected; we estimate through a lin-
ear regression fit that 5.74% ±1.46% of both symptomatic and
asymptomatic imported infections are detected. Nonetheless,
model projections are highly correlated with the observed data
(Pearson’s r= 0.93,P<0.0001), as shown in Fig. 5C,Inset. A
further validation of the model is provided by the reported num-
ber of ZIKV cases of pregnant women in the USA. A high
detection rate is expected in this closely monitored population.
As of September 29, 2016, 837 pregnant women in the USA
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AB
C
Fig. 5. (A) Correlation between the number of ZIKV cases by state in Colombia as reported by surveillance data through October 1, 2016 (38), compared
with state-level model projections of infections (median with 95% CI). Pearson’s rcorrelation coefficient is reported for the linear association on the log
scale. The outlier (in dark green) excluded from the statistical analysis corresponds to the Arauca region. (B) Timeline of microcephaly cases in Brazil through
April 30, 2016. Bar plots show weekly definite (or highly probable cases) and moderately (or somewhat probable cases) from surveillance data (40). Line plots
indicate estimated weekly new microcephaly cases given three levels of first trimester risk: 4.52% (circles) (37), 2.19% (squares) (37), and 0.95% (diamonds)
(36). (C) Bar plot of ZIKV infections imported into the USA by state(s) as reported by CDC surveillance through October 5, 2016 (41), and compared to
model projections (median with 95% CI) for the same period assuming 5.74% reporting/detection. (Inset) The correlation between CDC surveillance data
and model projections (median with 95% CI).
were laboratory-confirmed for ZIKV, all of whom were imported
cases. Because pregnant women comprise ∼1% of incoming air-
line traffic flow from the rest of the Americas (42), one can
roughly estimate 83,700 infections. Although this is a rough
estimate, because of fluctuations in pregnant women traffic flow
and testing rates, it is in the ballpark of our modeling results pro-
jecting 57,910 (95% CI [50, 138 to 66, 608]) infections imported
into the USA by early October 2016. These results are relevant
for ZIKV risk assessment in the USA (43, 44). In SI Appendix we
provide additional validation tests by looking at case reporting in
Brazil at the state level, and the detection of travel related cases
in European countries.
Discussion
We use computational modeling to reconstruct the past and
project the future spatiotemporal spread of ZIKV in the Amer-
icas. To identify the likely date and location of ZIKV’s first
introduction to the Americas, posterior densities are estimated
for 12 major travel hubs in Brazil over a range of dates. The
marginal posterior distributions suggest an introduction between
August 2013 and April 2014 in a number of potential locations,
including Rio de Janeiro, Brasilia, Fortaleza, and Salvador. This
date range overlaps with that suggested by a recent phyloge-
netic analysis (nextstrain.org/zika; ref. 30), although our estimate
also includes later potential introductions. The model seems to
rule out an introduction concurrent to the Soccer World Cup in
June 2014.
The model is able to generate epidemic curves in time for inci-
dent ZIKV cases for about two dozen countries in the Americas.
Although for the sake of space we report on only eight countries,
the full database is publicly available (www.zika-model.org). The
results obtained are in good agreement with model-based projec-
tions achieved with a different approach developed by Perkins
et al. (32) using location-specific epidemic ARs on highly spa-
tially resolved human demographic projections. Although the
approach of Perkins et al. (32) does not provide information on
the dynamic of the epidemic, it estimates ZIKV infections in the
first-wave epidemic in the most-affected countries such as Brazil
and Colombia, where the approach projects a median infection
AR of 19 and 14%, respectively, which falls within the CI of the
results provided here.
Although the initial introduction of ZIKV could date back to
August 2013, most countries did not experience the first wave of
the epidemic until the early months of 2016. Brazil is the only
country that seems to have a well-defined first peak in March
2015, consistent with reports from the northeast region (45). The
model suggests two epidemic waves in Brazil. The first wave,
occurring between January and July 2015, corresponds to early
outbreaks in the northeast region (Maranhao, Bahia, and Rio
Grande do Norte) and later on in the rest of the country. This
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first wave was not recognized as ZIKV until early 2016. The sec-
ond wave, between January and May 2016, affected mostly south-
ern states in Brazil (46). This progression of the epidemic is in
agreement with the reconstruction of the movement of ZIKV in
Brazil using confirmed cases at the municipal level (33).
The virus also circulated early on in the Caribbean, with ZIKV
samples isolated in Haiti at the end of 2014, and a possible
first peak occurred in October 2015 (47). Colombia first isolated
ZIKV in October 2015, at which time it spread rapidly from the
Caribbean coast to cities infested with A. aegypti (48). The model
suggests an introduction to Colombia as early as March–April
2015, potentially overlapping with the Easter holiday, which is
a period of high mobility within and between countries in the
region. ZIKV transmission in Venezuela follows a similar trajec-
tory, first isolated in November 2015 and present in all states by
July 2016 (49). Since March 2016, reported cases have declined
in both countries, consistent with our model estimates.
Our model estimates ZIKV transmission in El Salvador and
Honduras increasing around July 2015. ZIKV was first detected
in El Salvador in November 2015 and in Honduras in December
2015 (50, 51). Although the first ZIKV infection was confirmed in
Puerto Rico in the last week of December 2015 (52), the model
estimates ZIKV transmission in Puerto Rico beginning around
August 2015. In Mexico, the first infection was reported to the
surveillance system at the end of November 2015 (53), although
circulation may have begun in September 2015.
The epidemic has moved slowly and is mostly constrained by
seasonality in ZIKV transmissibility. Seasonal drivers and time
of introduction result in multiple waves (54) across several coun-
tries, as projected for Brazil, Honduras, and Mexico. To show the
importance of the seasonal drivers in shaping the epidemic, we
report in SI Appendix the analysis of two counterfactual scenar-
ios in which we eliminate the differences in the seasonal drivers
across the region. This analysis clearly shows that ignoring the
spatial variation of seasonal drivers gives rise to unrealistic pat-
terns incompatible with the observed data.
Another relevant result of the model is that incidence rates
dramatically decrease in all considered countries by the end
of 2016. The drop in incidence in the model is largely due to
the epidemic’s depleting the susceptible pool. This implies that
ZIKV epidemics could settle into the typical seasonal pattern
of mosquito-borne diseases such as DENV. Transmission may
be low for several years with a gradual buildup in susceptibil-
ity due to births (55). In the real world, however, other factors
such as vector control and/or specific local weather conditions
could have contributed to the drop of incidence along with herd
immunity. Because these factors might change in the future, sub-
sequent epidemic waves may occur. Precise projection of long-
Fig. 6. Schematic representation of the integration of data layers and the computational flow chart defining the GLEAM model for ZIKV.
term ZIKV transmission is crucial to plan for future Zika control
activities and for finding sites for phase-III Zika vaccine trials.
This is a topic for future research.
Another prominent feature emerging from the numerical
results is the extreme heterogeneity in the infection ARs across
countries. We find more than a sevenfold difference between
Honduras and Mexico, exhibiting infection ARs of 35% (95%
CI [30 to 39%]) and 5% (95% CI [4 to 6%]), respectively. These
large differences in infection ARs, which are also observable at
finer geographical resolutions, stem from variation in climatic
factors, mosquito densities, and socioeconomic factors.
We project the numbers of births from women who were
infected with ZIKV during the first trimester of their pregnancy.
There is a well-defined time lag between the epidemic curve and
this birth curve. Brazil, which likely experienced its first ZIKV
epidemic peak in March 2015, had a sharp rise in microcephaly
cases in September 2015, consistent with what was observed in
the field (40). In Colombia 132 confirmed cases of congenital
Zika syndrome had been observed as of March 11, 2017 (56).
However, at the same date, 538 additional cases are under study,
thus not yet allowing a risk factor estimate from the model.
Note that the projected number of microcephaly cases estimated
by the model varies considerably depending on the assumed
first-trimester risk, for which only retrospective estimates are
available (36, 37). We also note that with as many as 80% of
ZIKV infections being asymptomatic (4, 39), most of ZIKV-
infected pregnant women giving birth may not have experienced
symptoms during pregnancy. Thus, clinicians should be cautious
before ruling out ZIKV as the cause of birth defects. The results
presented here, however, could be used as a baseline to uncover
possible disagreement with the observed data and highlight the
need for additional key evidence to enhance our understanding
of the link between ZIKV and birth defects (57).
Available data on the ZIKV epidemic suffer from several
limitations. Although the disease has likely been spreading in
the Americas since late 2013, infection detection and report-
ing began much later and likely increased after the WHO’s
declaration of a PHEIC in February 2016. Case reporting is
inconsistent across countries. Furthermore, comparatively few
infections are laboratory-confirmed; this presents an additional
challenge because symptomatic cases with other etiologies
may be misdiagnosed, and asymptomatic infections are almost
entirely missed. Once a reliable ZIKV antibody test is avail-
able, seroprevalence studies can help determine the full extent of
these outbreaks. For external validation, we compare modeling
results with data from Brazil, Colombia, and the USA that were
not used to calibrate the model. We are able to replicate rel-
ative trends, although we estimate significantly higher absolute
Zhang et al. PNAS Early Edition |7 of 10

numbers, suggesting reporting and detection rates ranging from
1% to about 6% depending on the country.
The modeling approach presented here is motivated by the
need for a rapid assessment of the ZIKV epidemic, and it con-
tains assumptions and approximations unavoidable due to the
sparsity of available data. As a result, transmission is modeled
assuming ZIKV behaves similarly to DENV and other mosquito-
borne diseases. This includes the use of some expressions for
temperature dependence of transmissibility that are modeled on
DENV data. Although this assumption is plausible, more data
specific to ZIKV are certainly needed. The model has been cal-
ibrated by using data from French Polynesia and the observed
epidemic peak in Colombia (±1 wk), as reported by Colombia’s
National Institute of Health (38); further research is needed to
provide ZIKV-specific parameter estimates and more accurate
local calibrations. Mosquito presence/absence maps are available
from published data but have limitations as detailed in the litera-
ture (32, 34, 58). Sexual and other modes of transmission are not
incorporated in the model. The sexual component of the trans-
mission, however, might acquire relevance in areas where the
mosquito-borne transmission has a small reproductive number
and low incidence (9–12, 59). The specific socioeconomic fea-
tures of airline travelers are also not included. Finally, we do not
model public health interventions to control the vector popula-
tion or behavioral changes due to increased awareness. These
results may change as more information becomes available from
ZIKV-affected regions to refine the calibration of the model.
Conclusions
The model presented here provides a methodological frame-
work for the analysis of the global spread of ZIKV. The model
captures the slow dynamic of the epidemic characterized by
heterogeneity in the infection AR as well as the temporal
pattern resulting from local weather, population-level character-
istics, and human mobility:
•The model yields a probability distribution for the time and
place of introduction of ZIKV in Brazil, generating a compre-
hensive picture of the past dynamics of the epidemic.
•The numerical simulations allow estimates of the spatiotem-
poral spread of ZIKV in the Americas through February 2017.
In particular, it provides estimates for the infection ARs and
epidemic timing in ZIKV affected countries.
•The integration of airline travel data allows the explicit esti-
mation of the number of travel-related cases into the USA
and other countries.
•The model allows estimation of the number of newborns
from women infected by ZIKV during the first trimester of
pregnancy and the potential number of microcephaly cases
through 2017 assuming different levels of risk. These projec-
tions could be checked against observed data in the future.
Although the modeling results should be interpreted cau-
tiously in light of the assumptions and limitations inherent to the
approach, the framework emerging from the numerical results
may help in the interpretation of observed surveillance data and
provide indications for the magnitude and timing of the epi-
demic, as well as aid in planning for international and local out-
break response, and for the planning of phase-III ZIKV vaccine
trial sites. The study presented here also provides a computa-
tional modeling framework that can potentially be generalized
to other Aedes-transmitted vector-borne diseases, such as dengue
and chikungunya.
Materials and Methods
Model Summary. To study spatiotemporal ZIKV spread, we use the Global
Epidemic and Mobility Model (GLEAM), a previously described individual-
based, stochastic, and spatial epidemic model (60–65). This model integrates
high-resolution demographic, human mobility, socioeconomic (gecon.yale.
edu), and temperature data (climate.geog.udel.edu/∼climate/html pages/
Global2011/GlobalTsT2011.html); because no human subject research/analy-
sis was performed, IRB approval was not required. Here we expanded
to incorporate data on Aedes mosquito density (58) and the association
between socioeconomic factors and population risk of exposure (32, 66).
Similar to previous arbovirus modeling approaches (18), we use a compart-
mental classification of the disease stages in the human and mosquito pop-
ulations, assigning plausible parameter ranges based on the available ZIKV
literature and assumed similarities between ZIKV and DENV.
Global Model for the Spread of Vector-Borne Diseases. The GLEAM model
is a fully stochastic epidemic modeling platform that uses real-world data
to perform in silico simulations of the spatial spread of infectious dis-
eases at the global level. GLEAM uses population information obtained
from the high-resolution population database of the Gridded Population
of the World project from the Socioeconomic Data and Application Cen-
ter at Columbia University (sedac.ciesin.columbia.edu). The model consid-
ers geographical cells of 0.25◦×0.25◦, corresponding to an approximately
25-km ×25-km square for cells along Earth’s equator. GLEAM groups cells
into subpopulations defined by a Voronoi-like tessellation of the Earth’s sur-
face centered around major transportation hubs in different urban areas.
The model includes over 3,200 subpopulations in roughly 230 different
countries (numbers vary by year).
Within each subpopulation, a compartmental model is used to sim-
ulate the disease of interest. The model uses an individual dynamic
where discrete, stochastic transitions are mathematically defined by chain
binomial and multinomial processes. Subpopulations interact through the
A
B
Fig. 7. (A) Compartmental classification for ZIKV infection. Humans can
occupy one of the four top compartments: susceptible, which can acquire
the infection through contacts (bites) with infectious mosquitoes; exposed,
where individuals are infected but are not able yet to transmit the virus;
infectious, where individuals are infected and can transmit the disease to
susceptible mosquitoes; and recovered or removed, where individuals are
no longer infectious. The compartmental model for the mosquito vector is
shown below. (B) Summary of the parameters of the model. Tdep denotes
parameters that are temperature-dependent. T, Gdep denotes parameters
that are temperature- and geolocation-dependent. Specific values for the
parameters can be found in refs. 2, 4, 18, 55, and 68–70.
8 of 10 |www.pnas.org/cgi/doi/10.1073/pnas.1620161114 Zhang et al.

PNAS PLUS
BIOPHYSICS AND
COMPUTATIONAL BIOLOGY
POPULATION
BIOLOGY
mechanistically simulated mobility and commuting patterns of disease car-
riers. Mobility includes global air travel (www.oag.com), and GLEAM sim-
ulates the number of passengers traveling daily worldwide using available
data on origin–destination flows among indexed subpopulations.
The transmissibility of vector-borne diseases is associated with strong spa-
tial heterogeneity, driven by variability and seasonality in vector abundance,
the temperature dependence modulating the vector competence, and the
characteristics of the exposed populations. Many locations, such as those at
high elevation, are not at risk for autochthonous ZIKV transmission simply
because the vector is absent. In other locations the vector may be present
but sustained transmission is not possible because of environmental factors
that affect the vector’s population dynamics, such as temperature or pre-
cipitation. Housing conditions, availability of air conditioning, and socio-
economic factors also contribute significantly to determining the fraction
of the population likely exposed to the vector. To extend the GLEAM model
to simulate vector-borne diseases, a number of new datasets with high spa-
tial resolution are integrated, including the following:
•Global terrestrial air temperature data: The global air temper-
ature dataset (climate.geog.udel.edu/∼climate/html pages/Global2011/
GlobalTsT2011.html) contains monthly mean temperatures at a spatial
resolution of 0.5◦×0.5◦. To match the spatial resolution of GLEAM’s
gridded population density map, the temperature for each population
cell is extracted from the nearest available point in the temperature
dataset. Daily average temperatures are linearly interpolated from each
population’s monthly averages.
•Global A. aegypti and A. albopictus distribution: The global A. aegypti
and A. albopictus distribution database provides uncertainty estimates
for the vector’s distribution at a spatial resolution of 5 km ×5 km (58).
•Geolocalized economic data: The geophysically scaled economic dataset
(G-Econ), developed by Nordhaus et al. (67), maps the per capita Gross
Domestic Product [GDP, computed at purchasing power parity (PPP)
exchange rates] at a 1◦×1◦resolution. To estimate the per capita gross
cell product at PPP rates, the amount is distributed across GLEAM cells
proportionally to each cell’s population size. The data have also been
rescaled to reflect 2015 GDP per capita (PPP) estimates.
These databases are combined to model the key drivers of ZIKV trans-
mission, as illustrated in combination with necessary parameters in Fig.
6. Temperature affects many important disease parameters, including the
time- and cell-specific values of R0, whose variation induces seasonality
and spatial heterogeneity in the model. Temperature data are also used
together with the mosquito presence distribution data to define the daily
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-
ble because of environmental factors. The human populations in these
cells are thus considered unexposed to ZIKV and susceptible individuals are
assigned an environmental rescaling factor, ren, as described SI Appendix,
section 3. Finally, we use historical data and G-Econ to provide a socio-
economic rescaling factor, rse, reflecting how exposure to the vector is
impacted by socioeconomic variables such as availability of air condition-
ing. The derivation of these rescaling factors is provided in SI Appendix,
section 3.
Once the data layers and parameters have been defined, the model
runs using discrete time steps of one full day to simulate the transmission
dynamic model (described in detail below), incorporating human mobil-
ity between subpopulations, and partially aggregating the results at the
desired level of geographic resolution. The model is fully stochastic and from
any nominally identical initialization (initial conditions and disease model)
generates an ensemble of possible epidemics, as described by newly gener-
ated infections, time of arrival of the infection in each subpopulation, and
the number of traveling carriers. The Latin square sampling of the initial
introduction of ZIKV in Latin America and the ensuing statistical analysis is
performed on 150,000 stochastic epidemic realizations. From those realiza-
tions we find the probability p(x) and p(x|θ), defined as the probability of
the evidence (the epidemic peak in Colombia as from surveillance data) and
the likelihood of the evidence given the parameters θspecifying the date
and location of introduction of ZIKV in Brazil. From those distributions we
can calculate the posterior probabilities of interest. The sensitivity analysis
for the others scenarios considers an additional 200,000 simulations in total.
ZIKV Transmission Dynamics. Fig. 7Adescribes the compartmental classifi-
cations used to simulate ZIKV transmission dynamics. Humans can occupy
one of four compartments: susceptible individuals SHwho lack immunity
against the infection, exposed individuals EHwho have acquired the infec-
tion but are not yet infectious, infected individuals IHwho can transmit
the infection (and may or may not display symptoms), and removed indi-
viduals RHwho no longer have the infection and are immune to further
ZIKV infection. We consider the human population size to be constant, that
is, SH+EH+IH+RH=NH. The mosquito vector population is described by
the number of susceptible SV, exposed EV, and infectious mosquitoes IV. The
transmission model is fully stochastic. Transitions across compartments, the
human-to-mosquito force of infection, and the mosquito-to-human force
of infection are described by parameters that take into account the specific
abundance of mosquitoes and temperature dependence at the cell level.
Exposed individuals become infectious at a rate H, which is inversely pro-
portional to the mean intrinsic latent period of the infection (68). These
infectious individuals then recover from the disease at a rate µH(18), which
is inversely proportional to the mean infectious period. The mosquito-to-
human force of infection follows the usual mass-action law and is the prod-
uct of the number of mosquitoes per person, the daily mosquito biting rate,
and specific ZIKV infection transmissibility per day, the mosquito-to-human
probability of transmission (69), and the number IVof infected mosquitoes.
Exposed mosquitoes transition to the infectious class at a rate V, which is
inversely proportional to the mean extrinsic latent period in the mosquito
population (2). Susceptible, exposed, and infectious mosquitoes all die at a
rate that is inversely proportional to the mosquito lifespan, µV(70). The
mosquito-to-human force of infection follows the usual mass-action law
in each subpopulation whose linear extension varies from a few miles to
about 50 miles depending on the population density and specific area of
the world. A full description of the stochastic model and the equations is
provided in SI Appendix.
A summary of the parameters defining the disease dynamics is reported
in Fig. 7B. The empirical evidence related to the ZIKV infection in both
human and mosquito populations is fairly limited at the moment. We have
performed a review of the current studies of ZIKV and collected plausible
ranges for these parameters. As in other studies, we have assumed that the
drivers of ZIKV transmission are analogous to those of DENV. In particular,
we have considered that mosquito lifespan, mosquito abundance, and the
transmission probability per bite depend on the temperature level.
Model Calibration. The calibration of the disease dynamic model is per-
formed by a Markov chain Monte Carlo analysis of data reported from
the 2013 ZIKV epidemic in French Polynesia (18). Setting the extrinsic and
intrinsic latent periods and the human infectious period to reference val-
ues and using average daily temperatures of French Polynesia, we estimate
a basic reproduction number at the temperature T=25◦C for French Poly-
nesia RFP
0=2.75 (95% CI [2.53 to 2.98]), which is consistent with other ZIKV
outbreak analyses (18, 31). Because the reproduction number depends on
the disease serial interval, we report a sensitivity analysis in SI Appendix con-
sidering the upper and lower extremes of plausible serial intervals. Briefly,
the estimated RFP
0values are 2.06 (95% CI [1.91 to 2.22]) and 3.31 (95%
CI [3.03 to 3.6]) for the shortest and longest serial intervals, respectively.
The R0values are in the range of those estimated from local outbreaks in
San Andres Island (R0=1.41) and Girardot, Colombia (R0=4.61) (71); how-
ever, it is worth recalling that the reproductive number depends on the
location and on time through seasonal temperature changes. The calibra-
tion in French Polynesia provides the basic transmissibility of ZIKV. However,
variations in temperature and mosquito abundance yield varying R0in each
subpopulation tracked by the model as discussed in SI Appendix.
ACKNOWLEDGMENTS. This work was supported by Models of Infec-
tious Disease Agent Study, National Institute of General Medical Sciences
Grant U54GM111274, European Commission Horizon 2020 CIMPLEX Grant
641191, and a Colombian Department of Science and Technology Fulbright-
Colciencias scholarship (to D.P.R.).
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10 of 10 |www.pnas.org/cgi/doi/10.1073/pnas.1620161114 Zhang et al.

The spread of Zika virus in the Americas:
SI Appendix
Qian Zhang1, Kaiyuan Sun
1,MatteoChinazzi1, Ana Pastore y Piontti 1,
Natalie E. Dean 2, Diana Patricia Rojas 3,StefanoMerler4, Dina Mistry 1,
Piero Poletti 5,LucaRossi6,MargaretBray
1, M. Elizabeth Halloran 7,8,
Ira M. Longini Jr.2, Alessandro Vespignani1,6
1Laboratory for the Modeling of Biological and Socio-technical Systems,
Northeastern University, Boston, MA 02115, USA
2Department of Biostatistics, College of Public Health and Health Professions,
University of Florida, Gainesville, FL 32611, USA
3Department of Epidemiology, College of Public Health and Health Professions,
University of Florida, Gainesville, FL 32611, USA
4Bruno Kessler Foundation, Trento, Italy
5Bocconi University, Milan, Italy
6Institute for Scientific Interchange Foundation, Turin, Italy
7Vaccine and Infectious Disease Division, Fred Hutchinson Cancer Research Center,
Seattle, WA 98109, USA
8Department of Biostatistics, University of Washington, Seattle, WA 98195, USA
1

Contents
1 ZIKV Transmission Dynamics 3
1.1 Temperature/Seasonal Dependent Parameters . . . . . . . . . . . . . . . . . . . . 4
1.2 Spatiotemporal Dependency and Seasonality . . . . . . . . . . . . . . . . . . . . . 5
1.3 MCMC Calibration for ZIKV Transmissibility and Sensitivity Analysis . . . . . . 5
2 Spatiotemporal dependence of the vector population 7
3 Population at risk of ZIKV exposure 8
4 Microcephaly Projection 11
5 Developmental cycle of Aedes mosquitoes 12
6 Sensitivity analysis 14
7 Counterfactual seasonality scenarios 31
8 Additional validation tests 33
9 Incidence map of ZIKV infections 34
Bibliography 36
2

1 ZIKV Transmission Dynamics
The human-vector chain-binomial model is based on an SEIR compartmentalization of human
populations and SEI compartmentalization of vector populations [1].
Humans can be in one of four compartments: susceptible individuals (SH) who lack immu-
nity against infection, exposed individuals (EH) who have acquired infection but are not yet
infectious, infected individuals (IH) who can transmit infection (and may or may not display
symptoms), and removed individuals (RH) who are no longer infected. People in the final com-
partment may recover and gain immunity or die. As we are considering a timescale of a few
years that is relatively short when compared to human demographic dynamics, we treat the
total human population size as constant, i.e. SH+EH+IH+RH=NH.
The transition of people between compartments is performed stochastically, based on various
biological factors. Following Ref. [2], susceptible humans transition to the exposed compartment
under the force of infection (H) which is proportional to the rate at which a particular human is
bitten by the infected mosquitoes (IV/N V), the parameter that accounts for the daily mosquito
biting rate and the specific transmissibility of ZIKV, and the temperature dependence of the
mosquito-to-human probability of transmission (TVH). By considering the factor kexpressing
the number of mosquitoes per person we have NH=NV/k, yielding a force of infection H=
kTVH
IV
t
NV. On average individuals stay in the exposed or infectious state for the duration of
the mean intrinsic latent period ✏1
Hand the mean infectious period µ1
H, respectively.
The vector population is divided into three compartments: susceptible (SV), exposed (EV),
and infectious (IV), respectively. The force of infection (V) governing the transition rate from
susceptible to exposed individuals among the vector population is proportional to the density
of infectious humans (IH/N H). On average mosquitoes are in the exposed state the mean
extrinsic latent period ✏1
V. The average lifetime of mosquitoes in each compartment µ1
Vvaries
across spatial locations and time of the year [3] as discussed in the next section. The overall
mosquito population is rescaled every day as shown in Sec. 2, and it is considered in equilibrium
during the daily integration step so that mosquito deaths are replaced by an equal number of
new susceptible mosquitoes. Similar to the force of infection from vector to human, the force
of infection from human to the vector, V, is a function of , the temperature dependence of
human-to-mosquito transmission (THV ), and the density of infectious humans ( IH
t
NH). We thus
have V=THV
IH
t
NH.
The coupled population equations describing the epidemic time evolution read as:
SH
t+1 =SH
tSH!EH(1)
EH
t+1 =EH
t+
SH!EHEH!IH(2)
IH
t+1 =IH
t+
EH!IHIH!RH(3)
RH
t+1 =RH
t+
IH!RH,(4)
3

and
SV
t+1 =SV
tSV!EV+
IV!SV+
EV!SV(5)
EV
t+1 =EV
tEV!SVEV!IV+
SV!EV(6)
IV
t+1 =IV
t+
EV!IVIV!SV.(7)
In the above expressions each term X!Yrepresent the number of human or vector indi-
viduals transitioning from state Xto state Y. Transitions are calculated according to chain
binomial processes X!Y=Binomial(X, pX!Y), and pX!Yare transition probabilities deter-
mined by the force of infection and the average lifetime of individuals in each compartment. We
assume memoryless discrete stochastic transition processes. It is worth stressing that the terms
IV!SV,
EV!SVare introduced to model the replenishment of mosquitoes after death.
By using the standard approach of Ref. [2], the basic reproduction number can be expressed
as:
R0=✏V
(✏V+µV)(µVµH)k2TVHTHV .(8)
It is worth remarking that the basic reproduction number varies in each location according to
the temperature and mosquitoes abundance.
1.1 Temperature/Seasonal Dependent Parameters
•Mosquito Lifespan: We base our mosquito lifespan and corresponding mortality rate on
temperature. The relationship between mortality rate and temperature is polynomial,
taking the form [3]:
µV(T)=0.3967 0.03912T+2.442 ⇥103T27.479 ⇥105T3+9.298 ⇥107T4.(9)
Considering temperature ranges from 0C to 40C, the resulting range of average lifespans
goes from just under 1 day up to 7.2days. The corresponding minimum and maximum
daily mortality rates for mosquitoes are 1 days1and 0.1389 days1, respectively.
•Temperature dependence of the transmission probability per bite: Both the mosquito-to-
human and human-to-mosquito probabilities of transmission are temperature dependent
for DENV [4]. We thus assume that also for ZIKV the mosquito-to-human transmission
probability sharply declines to zero at T= 28C. When TVH(T) is close to zero, THV (T)
becomes less relevant. The virus will not continue to circulate if the mosquitoes can no
longer infect humans, even if the reverse transmission probability is one. Therefore, for
simplicity, we consider THV (T)=TVH(T) and use the expression for TVH to describe both:
TVH =0.001044T(T12.286)p32.461 T. (10)
We also note that in principle the number of bites per day is not constant. We have found
reports for Puerto Rico [5], showing a non-statistically relevant association, while there
is a mild dependence in Thailand [5]. In addition, the number of blood meals per day
seems to be constant across di↵erent seasonal cycles. Given our focus on the Americas
we decided to assume the results from Puerto Rico. Furthermore blood meal variations
appears to be a relatively minor contribution to the many temperature dependent factors
a↵ecting the behavior of the model [6].
4

•Seasonal variation of mosquito abundance: For areas with distinct seasonality, the vector
abundance may vary significantly from season to season due to temperature, vector life
cycle, etc. In the following, we consider a temporal modulation function kb(t)todescribe
the relative abundance modulation throughout the year in each subpopulation bconsidered
in the model, as detailed in Sec. 2.
1.2 Spatiotemporal Dependency and Seasonality
The di↵erent values of the parameters and mosquitoes per person in each subpopulation con-
sidered in the model yield a functional dependence of the basic reproduction number, R0,b(t),
in each subpopulation bat time tthat reads as:
R0,b(t)= ✏V
(✏V+µV(Tb,t)) (µV(Tb,t )µH)kb(Tb,t)2TVH(Tb,t)THV (Tb,t),(11)
where Tb,t is the average temperature in subpopulation bat time t. The variable R0,b(t) has
distinct temporal and geographical variations as shown in Fig. 3 of the main article. Therefore,
the seasonal and local drivers have the potential to shape both the timing and the magnitude
of ZIKV outbreaks.
1.3 MCMC Calibration for ZIKV Transmissibility and Sensitivity Analysis
The calibration of the model is performed using surveillance data from the 2013 ZIKV outbreak
in French Polynesia. The dataset is based on weekly situation reports from the Centre d’Hygiene
et de Salubrit´e Publique [1, 7, 8]. The reported number of new weekly suspected ZIKV cases
is available for each of the six main regions of French Polynesia: Tahiti, Sous-le-vent, Moorea,
Tuamotu, Marquises, and Australes. However, since there are no evident temporal separations
between the outbreaks of di↵erent regions, the regional data is aggregated to obtain the overall
weekly reported number of new suspected ZIKV cases in French Polynesia. We consider a
deterministic version of the model, reported in Sec 1 with the same notation.
There are 8 parameters in the infection dynamic model:
•Intrinsic latent period 1/✏H,
•Extrinsic latent period 1/✏V,
•Human infectious period 1/µH,
•Mosquito life span 1/µV,
•Number of mosquitoes per person k,
•ZIKV transmissibility ,
•Human-to-mosquito temperature dependence of the transmissibility THV , and
•Mosquito-to-human temperature dependence of the transmissibility TVH.
5

Unfortunately many parameters characterizing ZIKV are surrounded by uncertainty. We set the
number of mosquitoes per person as a constant k=kFP. A sensitivity analysis using di↵erent
values of kFP in the range of [1 3] has been performed. It must be noted that, all other
parameters being equal, variations in kare absorbed by a rescaling of the parameter .The
mosquito life span is temperature-dependent and using equations in Sec. 1.1, along with the
typical temperature during 2013 French Polynesia outbreak, we estimated that 1/µV=7.16
days.
The parameters 1/✏H,1/✏V,1/µH, and 1/µVdefine the serial interval of the infection. We
have considered di↵erent parameter sets that define one reference scenario along with short and
long serial interval scenarios which explore the range of parameters reported in the literature.
The values of the parameters are reported in Fig. 7b) of the main text. Assuming THV 'T
VH
and utilizing the fact that and THV (TVH) always appear together on both sides of the force
of infection, and THV are calibrated together into the overall transmissibility ˜
=THV .
The initial conditions at time t= 0 for the number of exposed humans EH
t0, the number of
exposed mosquitoes EV
t0, the infected humans IH
t0, and the infected mosquitoes IV
t0allow us to
numerically solve the infection dynamics. The cumulative number of infections Ctcan thus be
obtained as: dCt=✏HEH
tdt. Thus the weekly new incidence ctis given by ct=CtCt1.
Here we use a negative binomial measurement model [9, 1] with mean ⇢ctand variance
⇢ct(r+⇢ct)/r;⇢is the reporting rate, defined as the proportion of infections (symptomatic and
asymptomatic) that gets reported as clinical cases; ris the dispersion parameter of the negative
binomial distribution used to fit the data. To narrow the parameter space even more, we assume
EH
t0=IH
t0and EV
t0=IV
t0. For each scenario, we are left with a total of five unknown parameters
that require calibration:
•overall transmission rate ˜
,
•initial number of infected humans IH
t0,
•initial number of infected mosquitoes IV
t0,
•reporting rate ⇢, and
•dispersion parameter r.
A random walk Metropolis-Hastings Markov Chain Monte Carlo (MCMC) algorithm is per-
formed to calibrate the parameters above. We assume no prior information available for these
parameters, thus a uniform prior is used. The joint posterior distribution of the parameters was
sampled from 200,000 MCMC iterations, after 100,000 burn-in steps. The marginal posterior
distribution of parameters for each scenario is shown in Fig. S1.
Once calibrated, the 2013 French Polynesia outbreak is used as the reference point to obtain
infection parameters in other geo-locations. Specifically, remains constant and independent of
geographical locations, while all other parameters are rescaled in each subpopulation according
to the daily temperature data, mosquito presence, and socioeconomic drivers, as shown in the
following sections.
6

B C
A
1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6
R0
0
1
2
3
4
5
6
PDF
2.06(1.91,2.22)
0.28 0.29 0.30 0.31 0.32 0.33 0.34 0.35
˜
β
0
10
20
30
40
50
60
70
80
PDF
0.31(0.3,0.32)
2.6 2.8 3.0 3.2 3.4 3.6 3.8 4.0 4.2
R0
0.0
0.5
1.0
1.5
2.0
2.5
3.0
PDF
3.31(3.03,3.6)
0.25 0.26 0.27 0.28 0.29 0.30 0.31 0.32
˜
β
0
10
20
30
40
50
60
70
PDF
0.28(0.27,0.29)
2.0 2.2 2.4 2.6 2.8 3.0 3.2 3.4
R0
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
PDF
2.75(2.53,2.98)
0.24 0.25 0.26 0.27 0.28 0.29 0.30 0.31 0.32
˜
β
0
10
20
30
40
50
60
70
80
PDF
0.29(0.27,0.3)
Figure S1: MCMC calibration based on the 2013-2014 French Polynesia outbreak [1]. A)
Marginal posterior distribution of the basic reproduction number R0and overall transmission
rate ˜
for the short serial interval scenario. The median R0and ˜
values are listed in the upper
left-hand corners of the top and bottom figures, respectively. B) Marginal posterior distribution
of the basic reproduction number R0and overall transmission rate ˜
for the reference serial
interval scenario. C) Marginal posterior distribution of the basic reproduction number R0and
overall transmission rate ˜
for the long serial interval scenario.
2 Spatiotemporal dependence of the vector population
The mosquito abundance, factored into the model through the number of mosquitoes per person,
is a quantity that depends on the geographical location and time of the year. Mosquito abun-
dance is crucial in defining the risk of ZIKV outbreaks, as well as temporal patterns. Here we
consider the data for Aedes mosquitoes presence collected in Ref. [10]. The Global Aedes aegypti
and Aedes albopictus distribution is provided at the fine spatial resolution of 5 ⇥5 km cells and
yields the uncertainty of Ae. aegypti/Ae. albopictus presence in each cell. At 0.25 ⇥0.25 degree
spatial resolution (25km⇥25km along Earth’s Equator), the cell used by GLEAM contains mul-
tiple measurements of vector presence uncertainty. A cell of GLEAM contains mmeasurement
of vector presence uncertainty, which are p1,p
2, ...p
m. We thus define an average vector presence
7

cin each cell of GLEAM, c=m1Pm
i=1 pi. The typical daily commuting range for humans is
about the size of a GLEAM population cell. The population within the cell can be considered
well-mixed, which means the entire population is exposed to the mosquitoes, but with a relative
probability of mosquito explosure cin each cell.
As the mosquito presence distribution does not consider seasonal variation, we have included
a monthly modulation function depending on the local temperature in each census area. This
function was obtained by simulating a density-dependent stochastic model, which mimics the
biological processes driving the developmental cycle of Ae. albopictus in a typical breeding site.
The model is reported in Sec. 5. The modulation function has the following form:
k(t)/exp((˜
T(t)25)2/50),(12)
where ˜
T(t)=P78
i=0 T(ti)/79, tis the time in days and T(t) is the average temperature on
day t. To obtain the absolute value of k(t) we need a rescaling constant kcthat provides the
variation of mosquitoes per person:
ki(t)=cikcexp((˜
T(t)25)2/50),(13)
where ciaccounts for the relative probability of exposure in cell i. Since the model is calibrated
on the 2013 ZIKV outbreak in French Polynesia, under the assumption that during the outbreak
the e↵ective number of mosquitoes per person in French Polynesia (FP) is equal to the value
kFP used in the MCMC calibration, we obtain the following expression for kc:
kc=kFP
cFP exp((˜
T(t⇤)25)2/50),(14)
where T(t⇤) is the average temperature during the French Polynesia outbreak and cFP is the
specific rescaling factor of the number of mosquitoes per person in French Polynesia. The above
calibration depends on the number of mosquitoes per person considered in French Polynesia.
This value however must be consistent with the MCMC calibration that rescales the vector
transmissibility accordingly. Since the MCMC procedure determines the R0characterizing the
outbreak in French Polynesia, variations of kFP are absorbed in the parameter ; as such, they
do not alter the relative reproduction number variation across geographical location and time.
We have explicitly considered values of kFP in the range 1 to 3, confirming the invariance of the
results under consistent rescaling of all parameters.
3 Population at risk of ZIKV exposure
The GLEAM model integrates the transportation dynamics at the level of subpopulation. Each
subpopulation bis defined by a group of cells ithat may have di↵erent local weather (for ex-
ample, due to the altitude) and socioeconomic attributes. This implies that only a fraction
of individuals belonging to each subpopulation is actually exposed to ZIKV and participates
in the global spreading of the infection. In the following we use an approach that bears some
resemblance the one used by Perkins et al. [11] in introducing socioeconomic factors, in that we
use economic data and correlate with the magnitude of known outbreaks. However, while in
8

Ref. [11] the analysis aims at rescaling the local reproductive number, we opted for a rescaling
of the population e↵ectively exposed to the disease. In order to compute the population at
risk, we must exclude from the exposed population, individuals belonging to cells where envi-
ronmental factors are not favorable to the spreading of ZIKV. In particular, for each cell i,if
the average reproductive number during the highest 180 days is less than one, the population is
not considered at risk for a self-sustaining outbreak. Thus for each subpopulation, the fraction
of population environmentally exposed to ZIKV is:
ren =Pi0ni0
Pini
,(15)
where i0denotes a cell at risk of ZIKV, niis the population of the cell considered and the
summation is over all cells iincluded in the subpopulation b.
However, many of the studies suggest that even if the environmental conditions are suitable
for arbovirus transmission, the population’s risk of exposure to mosquitoes may still vary due to
socio-economic heterogeneities [12, 11, 13]. For example, di↵erent socio-economic factors, such
as improved sanitation facilities, the fraction of the population living in extreme poverty, use of
air conditioning in buildings, housing conditions, education level, and level of employment, may
alter the arbovirus exposure risk. All of those factors are in general strongly correlated with the
level of economic development of the geographical region under study.
For this reason, we have only considered arbovirus outbreaks in na¨ıve populations for which
reliable estimates are available for both the final infection attack (ARf inal), which is generally ob-
tained through seroprevalence studies, and the ideal infection attack rate (ARideal), which is com-
puted when only environmental factors are considered. The ratio rse =ARf inal/ARideal provides
a proxy for the fraction of exposed population that we can associate with the geographically-
based version of the per capita Gross Domestic Product based on Purchasing Power Parity rates
(GDP per capita, PPP) which is in turn used to capture the socio-economic di↵erences that
exist across and within countries. Each cell is then assigned a Gross Cell Product (GCP) by
allocating the subpopulation GDP proportionally to the population sizes of the cells within this
subpopulation. We find that the above association is well approximated by the relation:
brse =b↵+b
log(GCP per capita, PPP),(16)
where b↵and b
are estimated using an ordinary least squares (OLS) regression based on the
outbreak reported in Fig. S2. The quantity brse is associated with the corresponding value of
the Gross Cell Product (GCP) per capita of each GLEAM cell, and it yields the fraction of
population actually exposed to ZIKV.
However, in our model simulations, we do not use the point estimate of brse . Rather, for each
cell, we consider 1,000 di↵erent values as drawn from the 95% prediction interval of the fitted
model. By doing so, we control for the fact that our regression model has been calibrated using
a limited amount of data and therefore introduce an additional element of stochasticity in our
simulations to account for the uncertainty related to our estimates.
In order to derive the fraction of population exposed to ZIKV in each subpopulation bwe
can consider all cells i|i2b. Let nidenote the population in cell i, and let rse,i denote the
9

1.0
0.8
0.6
0.4
0.2
0.0
Risk of Exposure
Gross Cell Product (GCP) per capita based on
Purchasing Power Parity (PPP) rates (log scale)
3.0
2.5 3.5 4.0 4.5
BA
Outbreak Location Attack Rate Ref.
Lamu Island Kenya
Grange Comore Island
Manajary, Madagascar
Mayotte
Reunion Island
Paramaribo, Suriname
Saint Martin
Castiglione de Cervia,
Italy
0.75
0.63
0.45
0.37
0.35
0.25
0.17
0.10
[14]
[15]
[16]
[12]
[17]
[18]
[19]
[20]
Figure S2: Risk of exposure as function of the Gross Cell Product (GCP) per capita (dashed line
and shaded area represent best fit and 95% CI separately). Attack rates of previous chikungunya
outbreak can be found in Refs. [14, 15, 16, 12, 17, 18, 19, 20]
fraction of people in cell iexposed to ZIKV for socio-economic reasons. The overall population
exposed to ZIKV in the subpopulation bis then:
Nexp
b=X
{i0}
rse,i0ni0,(17)
where i0are the cells environmentally exposed to ZIKV.
Within each subpopulation bonly exposed individuals Nexp
bare considered in the infection
transmission dynamic, while the entire population Nbis considered in the mobility process. The
baseline level ZIKV infection dynamic works at the homogeneous mixing level, and quantities
are thus averaged over the environmentally exposed cells:
cb=P{i0}ci0rse,i0ni0
Nexp
b
,(18)
and
Tb(t)=P{i0}Ti0(t)rse,i0ni0
Nexp
b
.(19)
The remaining spatio-temporal dependent infection parameters at the subpopulation level can
be calculated accordingly. In Fig. S3 we show a schematic representation of the process of
computing the remaining population in each cell of GLEAM. Starting from the original cell’s
population in GLEAM, the GECON, and Aedes mosquitoes distribution data act like filters for
the population at risk through ren and rse .
The spatial heterogeneities of population at risk due to environmental and socio-economic
factors also a↵ect the di↵usion of disease among subpopulations. A person exposed or infected
10

100 km
São Paulo
Remaining population
low high
GECON
Aedes mosquito
distribution
Rio de Janeiro
GLEAM
GLEAM subpopulation
Figure S3: Schematic representation of the process of computing the remaining population
for each subpopulation in GLEAM. Starting from the original cell’s population in GLEAM, the
GECON and Aedes mosquito distribution data act like filters for the population at risk through
ren and rse.
with ZIKV who travels from a subpopulation experiencing an on-going outbreak will not be
able to seed the epidemic in the subpopulation of travel destination, if his or her destination is
not at risk of ZIKV due to environmental or socioeconomic factors. Specifically, in the model,
assuming the fraction of exposed population in destination subpopulation bis Nexp
b/Nb,the
probability of a traveling ZIKV carrier entering an area where the population is exposed to
ZIKV and participating in the transmission dynamics is Nexp
b/Nb. Conversely, the probability
of a traveling ZIKV carrier entering the area where the population is not exposed to ZIKV
and isolated from further transmission is 1 Nexp
b/Nb. It is worth noticing that by focusing
on the fraction of e↵ectively exposed population, even in places where economic factors can be
extremely favorable it is possible to have smalls outbreaks. A clear example of this situation is
the ZIKV outbreak in the US.
4 Microcephaly Projection
The projection of potential microcephaly cases related to ZIKV follows the model proposed
in the study of ZIKV-microcephaly association of 2013-2014 French Polynesia outbreak [21].
Specifically, we used a first trimester model: if a woman is infected with ZIKV during the first
trimester of her pregnancy, the risk of microcephaly associated with ZIKV is pmduring the first
trimester and 0 otherwise. For simplicity, we use a pregnancy model with a fixed duration of
pregnancy of 40 weeks; neither miscarriage nor termination of pregnancy is considered. Given
11

the weekly birth rate rb[22] and weekly new ZIKV infections c(t) in an administrative area with
population N, the number of women beginning a pregnancy in a given week is:
np=Nrb.(20)
The probability of a woman being infected with ZIKV during the first trimester of her
pregnancy is:
pz(t)=Pt+ttrim1
t0=tc(t0)
N,(21)
where ttrim1= 13 weeks is the length of first trimester.
Thus, the projected number of microcephaly cases of a given week is given by:
nm(t+tpreg )=np⇥pz(t)⇥pm=Nrb⇥pm⇥Pt+ttrim1
t0=tc(t0)
N,(22)
where tpreg = 40 weeks is the duration of pregnancy.
Equation 22 establishes the relationship between number of new ZIKV cases c(t) and pro-
jected number of new microcephaly cases nm(t).
5 Developmental cycle of Aedes mosquitoes
We estimate a temperature modulation function that reproduces the seasonal pattern of female
adult mosquitoes. The proposed approach is based on a model previously used to estimate
the abundance of female adults of Ae. albopictus during the 2007 chikungunya outbreak in
Emilia Romagna (Italy) [23]. Briefly, the model mimics the biological processes driving the full
developmental cycle of Ae. albopictus in a typical breeding site, explicitly accounting for egg
hatching, pupation, adult emergence, and for the adult life cycle of alternate feeding and laying
of eggs (gonotrophic cycle). The developmental rates from one stage to the next, the duration
of the gonotrophic cycle, and the mortality rates of di↵erent life stages depend on the average
daily temperature [24]. The temporal dynamics of eggs (E), larvae (L), pupae (P), and female
adults (A) is described by the following equations:
E0=ne
1
gA✓1E
K◆µeEdeE
L0=deEdlLµlL(23)
P0=dlLdpPµpP
A0=1
2dpPµaA,
where neis the number of eggs laid in one oviposition, gis the duration of gonotrophic cycle,
Kdrives the carrying capacity for the eggs, µe,µ
l,µ
p,µ
aare the death rates associated with
di↵erent stages of the mosquitoes and de,d
l,d
pare the developmental rates driving the transitions
of vectors across the di↵erent mosquito life stages; the 1/2 term in the last equation accounts
for a 1:1 sex ratio of adult mosquitoes.
12

Mean daily air temperature (°C)
Mosquito density
(number per ha)
0
500
1000
1500
2000
2500
3000
0 5 10 15 20 25 30
Day of the year
Mosquito density
(number per ha)
0
30
60
90
120
150
180
210
240
270
300
330
360
0
500
1000
1500
2000
2500
3000
0
5
10
15
20
25
30
Mean daily air temperature (°C)
0
500
1000
1500
2000
2500
0 5 10 15 20 25 30 35
Day of the year
0
30
60
90
120
150
180
210
240
270
300
330
360
0
500
1000
1500
2000
2500
3000
0
5
10
15
20
25
Mosquito density
(number per ha)
Mosquito density
(number per ha)
T(79) (°C)
~
T(79) (°C)
~
A B
DC
Figure S4: A) Average mosquito density at di↵erent temperatures as estimated by model
simulation (grey points). Fitted average mosquito density at di↵erent temperatures, by assuming
the following relationship: D(T) = 2500exp{(T32)2/150}(cyan line). B) Mean daily air
temperature over time (blue line). Average mosquito density as estimated by model simulation
(cyan line). Predicted mosquito density over time, by assuming the following relationship:
D(T) = 2500exp{(T32)2/150}(green line). C) Average mosquito density at di↵erent
temperatures as estimated by model simulation (grey points). Fitted average mosquito density
at di↵erent temperature values of ˜
T=P78
i=0 T(ti)/79, by assuming the following relationship:
D(˜
T) = 2300exp{(˜
T25)2/50}(cyan line). D) Mean temperature values of ˜
Tover time
(blue line). Average mosquito density as estimated by model simulation (cyan line). Predicted
mosquito density over time, by assuming the relationship following: D(˜
T) = 2300exp{(˜
T
25)2/50}(green line).
The simulated average abundance of female adult mosquitoes within a breeding site is dis-
played in Fig S4 A), along with the average daily air temperature observed in Emilia Romagna
during 2007. The expected density of adult mosquitoes at di↵erent temperatures were estimated
by computing for each degree of temperature T between 0C–30C the mean number of female
adults predicted among days characterized by an average daily temperature within the range
defined by T-0.5C and T+0.5C. Since high temperature reduces the mosquito survival rate
(especially in adults), and low temperature prevents the development of immature stages into
adults, the mosquito density is expected to be lower at both low and high temperature regimes.
We therefore fit a Normal density function to the expected number of adult mosquito at di↵er-
ent temperatures. Obtained results are shown in Fig S4B. The described procedure provides a
modulation function of temperature that is used to approximate the seasonality of the mosquito
13

abundance.
As shown in Fig S4 B) the proposed approximation overestimates the abundance of the
vector in spring (i.e. at the beginning of the breeding season), and underestimates the mosquito
density in autumn. In fact, this procedure does not account for two critical factors. The first one
is that adult abundance depends on the persistence of favorable temperature conditions during
the whole life cycle of the mosquito’s development. The second one is that the mosquito density
at a given time is influenced by the vector abundance in the preceding generations. We therefore
investigated the relationship between the density of adult mosquitoes at a given time twith the
mean air temperature recorded between ttand t. In particular, we considered di↵erent
values of t, ranging from 1 to 365 days and fit separately for each value of ta Normal density
function to the expected abundance of vectors at di↵erent values of ˜
T(t)=Pt
i=0 T(ti)/t(see
Fig S4C). Results show that the best approximation of the adult mosquito density is obtained
when a time window of 79 days is considered. The proposed approach provides a suitable
modulation function to reproduce seasonal patterns characterizing the relative abundance of
adult mosquitoes over time by using temperature values only (see Fig S4 D).
6 Sensitivity analysis
In the following we report sensitivity analyses that are calibrated according to three di↵erent
scenarios.
•Aegypti scenario. This scenario considers Ae. aegypti as the only competent ZIKV vector.
The parameters describing the infection are set in the middle of the range of the estimates
in the literature.
•Short serial interval scenario. This scenario considers both Ae. aegypti and Ae. albopictus
as competent ZIKV vectors. The parameters describing the infection are set in order to
explore the shortest serial interval allowed by the range of parameters reported in the
literature.
•Long serial interval scenario. This scenario considers both Ae. aegypti and Ae. albopictus
as competent ZIKV vectors. The parameters describing the infection are set in order
to explore the longest serial interval allowed by the range of parameters reported in the
literature.
The three additional scenarios described above, when compared to the reference scenario,
provide similar posterior distributions of location and time of introduction in Brazil. The most
likely time of introduction is between October and December 2013, and the most likely location
of introduction is Rio de Janeiro for all three scenarios. The timing and profile of Zika/births
with first trimester ZIKV infections resemble the reference scenario as well. Variations are
observed for the country level ZIKV infection ARs (by February 28, 2017). This is clearly due
to the change of the reproductive number in the case of longer or shorter serial interval and to the
di↵erence in mosquitoes’ presence in the case that only Ae. aegypti is a competent vector. Figure
S5 summarizes the changes in the three additional scenarios when compared to the reference
scenario.
14

short both scenario
median aegypti scenario
reference scenario
long both scenario
Figure S5: Comparison of ZIKV infection ARs between reference scenario and three
additional scenarios: Projected ZIKV infection ARs(Median estimates) and 95% CI through
February 28, 2017 for the Reference scenario, Aegypti scenario, Short serial interval scenario,
Long serial interval scenario, in eight a↵ected countries in the Americas. ZIKV attack rates
include asymptomatic infections. The denominator is the entire country population, including
regions that are not exposed to the vector.
15

Aegypti scenario
B
A
C
2013 2014
2013 2014
Figure S6: Aegypti Scenario: Posterior distribution for ZIKV introductions in twelve major
transportation hubs in Brazil between April 2013 and June 2014, incorporating the likelihood of
replicating the observed epidemic peak in Colombia. A) Full posterior distribution as a function
of location and time of introduction. B) Marginal posterior distribution for time (month) of
introduction. C) Marginal posterior distribution for location of introduction.
16

Figure S7: Aegypti Scenario: Estimated daily number of new ZIKV infections (per 1000
people) in eight a↵ected 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, respectively. 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. *Puerto Rico curves are constrained under the condition that the peak of incidence
curve is after March 1, 2016, based on surveillance data [25].
17

Figure S8: Aegypti Scenario: Estimated daily number of births between October 2014 and
December 2017 from women infected with ZIKV during the first trimester of pregnancy in eight
a↵ected countries 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
with a di↵erent scale. The median curve 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.
18

Feb. 1, 2016 Feb. 28, 2016 Feb. 1, 2016 Dec. 10, 2017 Feb. 1, 2016 Dec. 10, 2017 Feb. 1, 2016 Dec. 10, 2017
Brazil 15 [ 12 - 16 ] 16 [ 14 - 17 ] 808 [ 186 - 1022 ] 1148 [ 1054 - 1240 ] 1863 [ 430 - 2357 ] 2647 [ 2429 - 2859 ] 3845 [ 887 - 4864 ] 5463 [ 5013 - 5901 ]
Colombia 3 [ 2 - 5 ] 9 [ 8 - 10 ] 0 [ 0 - 5 ] 167 [ 147 - 191 ] 1 [ 0 - 12 ] 386 [ 339 - 440 ] 1 [ 0 - 26 ] 796 [ 699 - 908 ]
Mexico 0 [ 0 - 2 ] 4 [ 2 - 5 ] 0 [ 0 - 9 ] 242 [ 133 - 299 ] 0 [ 0 - 21 ] 557 [ 307 - 689 ] 0 [ 0 - 43 ] 1151 [ 634 - 1423 ]
2 [ 0 - 6 ] 20 [ 14 - 26 ] 0 [ 0 - 0 ] 19 [ 14 - 25 ] 0 [ 0 - 0 ]
43 [ 31 - 57 ] 0 [ 0 - 0 ]
88 [ 65 - 118 ]
El Salvador 0 [ 0 - 3 ] 12 [ 7 - 15 ] 0 [ 0 - 0 ] 29 [ 18 - 37 ] 0 [ 0 - 0 ] 67 [ 41 - 85 ] 0 [ 0 - 0 ] 139 [ 84 - 175 ]
Honduras 1 [ 0 - 15 ] 32 [ 20 - 36 ] 0 [ 0 - 0 ] 130 [ 83 - 151 ] 0 [ 0 - 1 ] 300 [ 192 - 347 ] 0 [ 0 - 2 ] 620 [ 396 - 717 ]
Haiti 37 [ 0 - 53 ] 48 [ 40 - 54 ] 0 [ 0 - 120 ] 306 [ 260 - 349 ] 0 [ 0 - 278 ] 706 [ 599 - 805 ] 0 [ 0 - 573 ] 1456 [ 1235 - 1661 ]
Venezuela 8 [ 1 - 18 ] 17 [ 15 - 19 ] 1 [ 0 - 61 ] 247 [ 216 - 283 ] 2 [ 0 - 141 ] 569 [ 498 - 653 ] 3 [ 0 - 291 ] 1174 [ 1029 - 1347 ]
(median with 95%CI)
Infection AR %
first trimester risk: 0.95% first trimester risk: 2.19% first trimester risk: 4.52%
Cumulative Microcephaly Cases (median with 95%CI)
Puerto Rico*
Figure S9: Aegypti Scenario: Projected ZIKV infection ARs through the time of the WHO
declaration of a PHEIC on February 1, 2016, and through February 28, 2017, in eight a↵ected
countries in the Americas. Median estimates and 95 % CIs are provided. ZIKV attack rates
include asymptomatic infections. The denominator is the entire country population, including
regions that are not exposed to the vector. Cumulative microcephaly cases due to ZIKV infection
during the first trimester of pregnancy through the time of the WHO declaration of a PHEIC on
February 1, 2016, and through December 10, 2017, in eight a↵ected countries in the Americas.
We consider three di↵erent risks of microcephaly associated with ZIKV infection during the
first trimester: 0.95% first trimester risk based on a study of the 2013-2014 French Polynesian
outbreak [21]; 2.19% (100% over-reporting) and 4.52% (no over-reporting) first trimester risks,
based on a study of Bahia, Brazil [26], given a model-estimated 29% infection AR in Bahia.
*Puerto Rico curves constrained under the condition that the peak of ZIKV incidence curve is
after March 1, 2016, based on surveillance data [25].
19

AB
C
2015 2016
Figure S10: Aegypti Scenario: A) Correlation between the number of ZIKV cases by state in
Colombia as reported by surveillance data through October 1, 2016 [27], compared with state-
level model projections of infections (median with 95 % CI). Pearson’s r correlation coefficient
is reported for the linear association on the log scale. The outlier (in dark green) excluded
from the statistical analysis corresponds to the Arauca region. B) Timeline of microcephaly
cases in Brazil though April 30, 2016. Bar plot shows weekly definite (or highly probable cases)
and moderately (or somewhat probable cases) from surveillance data [28]. Line plots indicate
estimated weekly new microcephaly cases given three levels of first trimester risk: 4.52% (round)
[26], 2.19% (square) [26], and 0.95% (diamond) [21]. C) Bar plot of ZIKV infections imported
into the continental USA by state(s) as reported by CDC surveillance through October 5, 2016
[29], and compared to model projections (median with 95 % CI) for the same period assuming
5.74% reporting/detection. The insert shows the correlation between CDC surveillance data
and model projections (median with 95 % CI).
20

Short serial interval scenario
B
A
C
2013 2014
2013 2014
Figure S11: Short Serial Interval Scenario: Posterior distribution for ZIKV introductions in
twelve major transportation hubs in Brazil between April 2013 and June 2014, incorporating the
likelihood of replicating the observed epidemic peak in Colombia. A) Full posterior distribution
as a function of location and time of introduction. B) Marginal posterior distribution for time
(month) of introduction. C) Marginal posterior distribution for location of introduction.
21

Figure S12: Short Serial Interval Scenario: Estimated daily number of new ZIKV infections
(per 1000 people) in eight a↵ected 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, respectively. 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. *Puerto Rico curves are constrained under the condition that the peak of
incidence curve is after March 1, 2016, based on surveillance data [25].
22

Figure S13: Short Serial Interval Scenario: Estimated daily number of births between
October 2014 and December 2017 from women infected with ZIKV during the first trimester of
pregnancy in eight a↵ected countries 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 with on di↵erent scale. The median curve 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.
23

Feb. 1, 2016 Feb. 28, 2017 Feb. 1, 2016 Dec. 10, 2017 Feb. 1, 2016 Dec. 10, 2017 Feb. 1, 2016 Dec. 10, 2017
Brazil 13 [ 10 - 15 ] 14 [ 12 - 16 ] 836 [ 234 - 1067 ] 1032 [ 914 - 1155 ] 1927 [ 539 - 2460 ] 2379 [ 2107 - 2662 ] 3978 [ 1113 - 5077 ] 4910 [ 4348 - 5495 ]
Colombia 4 [ 2 - 6 ] 9 [ 7 - 10 ] 1 [ 0 - 25 ] 161 [ 135 - 188 ] 1 [ 0 - 59 ] 370 [ 312 - 434 ] 3 [ 0 - 121 ] 765 [ 645 - 896 ]
Mexico 0 [ 0 - 2 ] 3 [ 1 - 4 ] 0 [ 0 - 19 ] 189 [ 37 - 259 ] 0 [ 0 - 43 ] 436 [ 85 - 597 ] 0 [ 0 - 89 ] 899 [ 175 - 1232 ]
Puerto Rico* 1 [ 0 - 6 ] 17 [ 11 - 25 ] 0 [ 0 - 0 ] 16 [ 11 - 24 ] 0 [ 0 - 0 ] 38 [ 25 - 54 ] 0 [ 0 - 0 ] 78 [ 51 - 112 ]
El Salvador 0 [ 0 - 9 ] 11 [ 4 - 13 ] 0 [ 0 - 0 ] 27 [ 9 - 33 ] 0 [ 0 - 1 ] 63 [ 21 - 77 ] 0 [ 0 - 1 ] 129 [ 42 - 159 ]
Honduras 1 [ 0 - 27 ] 29 [ 15 - 34 ] 0 [ 0 - 9 ] 120 [ 62 - 140 ] 0 [ 0 - 21 ] 276 [ 143 - 323 ] 0 [ 0 - 43 ] 569 [ 296 - 666 ]
Haiti 38 [ 0 - 49 ] 44 [ 38 - 50 ] 0 [ 0 - 187 ] 284 [ 242 - 320 ] 0 [ 0 - 430 ] 654 [ 558 - 738 ] 0 [ 0 - 888 ] 1349 [ 1152 - 1522 ]
Venezuela 11 [ 2 - 16 ] 15 [ 13 - 18 ] 3 [ 0 - 157 ] 222 [ 191 - 256 ] 8 [ 0 - 362 ] 511 [ 440 - 591 ] 16 [ 0 - 747 ] 1054 [ 908 - 1220 ]
(median with 95%CI)
Infection AR %
first trimester risk: 0.95% first trimester risk: 2.19% first trimester risk: 4.52%
Cumulative Microcephaly Cases (median with 95%CI)
Figure S14: Short Serial Interval Scenario: Projected ZIKV infection ARs through the
time of the WHO declaration of a PHEIC on February 1, 2016, and through February 28,
2017, in eight a↵ected countries in the Americas. Median estimates and 95 % CIs are provided.
ZIKV attack rates include asymptomatic infections. The denominator is the entire country
population, including regions that are not exposed to the vector. Cumulative microcephaly
cases due to ZIKV infection during the first trimester of pregnancy through the time of the
WHO declaration of a PHEIC on February 1, 2016, and through December 10, 2017, in eight
a↵ected countries in the Americas. We consider three di↵erent risks of microcephaly associated
with ZIKV infection during the first trimester: 0.95% first trimester risk based on a study of the
2013-2014 French Polynesian outbreak [21]; 2.19% (100% over-reporting) and 4.52% (no over-
reporting) first trimester risks, based on a study of Bahia, Brazil [26], given a model-estimated
27% infection AR in Bahia. *Puerto Rico curves constrained under the condition that the peak
of ZIKV incidence curve is after March 1, 2016, based on surveillance data [25].
24

AB
C
2015 2016
Figure S15: Short Serial Interval Scenario: A) Correlation between the number of ZIKV
cases by state in Colombia as reported by surveillance data through October 1, 2016 [27],
compared with state-level model projections of infections (median with 95 % CI). Pearson’s r
correlation coefficient is reported for the linear association on the log scale. The outlier (in dark
green) excluded from the statistical analysis corresponds to the Arauca region. B) Timeline
of microcephaly cases in Brazil though April 30, 2016. Bar plot shows weekly definite (or
highly probable cases) and moderately (or somewhat probable cases) from surveillance data
[28]. Line plots indicate estimated weekly new microcephaly cases given three levels of first
trimester risk: 4.52% (round) [26], 2.19% (square) [26], and 0.95% (diamond) [21]. C) Bar
plot of ZIKV infections imported into the continental USA by state(s) as reported by CDC
surveillance through October 5, 2016 [29], and compared to model projections (median with 95
% CI) for the same period assuming 5.74% reporting/detection. The insert shows the correlation
between CDC surveillance data and model projections (median with 95% CI).
25

Longserial interval scenario
B
A
C
2013 2014
2013 2014
Figure S16: Long Serial Interval Scenario: Posterior distribution for ZIKV introductions in
twelve major transportation hubs in Brazil between April 2013 and June 2014, incorporating the
likelihood of replicating the observed epidemic peak in Colombia. A) Full posterior distribution
as a function of location and time of introduction. B) Marginal posterior distribution for time
(month) of introduction. C) Marginal posterior distribution for location of introduction.
26

Figure S17: Long Serial Interval Scenario: Estimated daily number of new ZIKV infections
(per 1000 people) in eight a↵ected 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, respectively. 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. *Puerto Rico curves are constrained under the condition that the peak of
incidence curve is after March 1, 2016, based on surveillance data [25].
27

Figure S18: Long Serial Interval Scenario: Estimated daily number of births between Oc-
tober 2014 and December 2017 from women infected with ZIKV during the first trimester of
pregnancy in eight a↵ected countries 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 with on di↵erent scale. The median curve 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.
28

Feb. 1, 2016 Feb. 28, 2017 Feb. 1, 2016 Dec. 10, 2017 Feb. 1, 2016 Dec. 10, 2017 Feb. 1, 2016 Dec. 10, 2017
Brazil 17 [ 15 - 19 ] 20 [ 18 - 21 ] 765 [ 144 - 1182 ] 1434 [ 1318 - 1558 ] 1763 [ 332 - 2725 ] 3306 [ 3038 - 3591 ] 3640 [ 685 - 5623 ] 6823 [ 6271 - 7412 ]
Colombia 5 [ 3 - 8 ] 13 [ 12 - 15 ] 0 [ 0 - 3 ] 245 [ 220 - 276 ] 0 [ 0 - 6 ] 565 [ 506 - 636 ] 1 [ 0 - 13 ] 1165 [ 1045 - 1313 ]
Mexico 1 [ 0 - 2 ] 6 [ 5 - 7 ] 0 [ 0 - 2 ] 367 [ 307 - 412 ] 0 [ 0 - 5 ] 845 [ 708 - 950 ] 1 [ 0 - 10 ] 1744 [ 1462 - 1961 ]
Puerto Rico* 2 [ 0 - 6 ] 20 [ 14 - 29 ] 0 [ 0 - 0 ] 19 [ 13 - 27 ] 0 [ 0 - 0 ] 44 [ 31 - 63 ] 0 [ 0 - 0 ] 92 [ 64 - 129 ]
El Salvador 2 [ 0 - 17 ] 20 [ 16 - 24 ] 0 [ 0 - 0 ] 50 [ 41 - 60 ] 0 [ 0 - 0 ] 114 [ 94 - 138 ] 0 [ 0 - 1 ] 236 [ 194 - 284 ]
Honduras 10 [ 0 - 32 ] 37 [ 33 - 41 ] 0 [ 0 - 1 ] 153 [ 135 - 171 ] 0 [ 0 - 3 ] 353 [ 311 - 395 ] 0 [ 0 - 7 ] 729 [ 642 - 816 ]
Haiti 46 [ 4 - 56 ] 51 [ 44 - 58 ] 0 [ 0 - 32 ] 329 [ 286 - 374 ] 0 [ 0 - 74 ] 759 [ 660 - 862 ] 1 [ 0 - 153 ] 1567 [ 1362 - 1779 ]
Venezuela 14 [ 6 - 20 ] 20 [ 18 - 22 ] 2 [ 0 - 61 ] 289 [ 257 - 329 ] 4 [ 0 - 140 ] 666 [ 592 - 758 ] 8 [ 0 - 288 ] 1375 [ 1222 - 1564 ]
(median with 95%CI)
Infection AR %
first trimester risk: 0.95% first trimester risk: 2.19% first trimester risk: 4.52%
Cumulative Microcephaly Cases (median with 95%CI)
Figure S19: Long Serial Interval Scenario: Projected ZIKV infection ARs through the time
of the WHO declaration of a PHEIC on February 1, 2016, and through February 28, 2017,
in eight a↵ected countries in the Americas. Median estimates and 95 % CIs are provided.
ZIKV attack rates include asymptomatic infections. The denominator is the entire country
population, including regions that are not exposed to the vector. Cumulative microcephaly
cases due to ZIKV infection during the first trimester of pregnancy through the time of the
WHO declaration of a PHEIC on February 1, 2016, and through December 10, 2017, in eight
a↵ected countries in the Americas. We consider three di↵erent risks of microcephaly associated
with ZIKV infection during the first trimester: 0.95% first trimester risk based on a study of the
2013-2014 French Polynesian outbreak [21]; 2.19% (100% over-reporting) and 4.52% (no over-
reporting) first trimester risks, based on a study of Bahia, Brazil [26], given a model-estimated
33% infection AR in Bahia. *Puerto Rico curves constrained under the condition that the peak
of ZIKV incidence curve is after March 1, 2016, based on surveillance data [25].
29

AB
C
2015 2016
Figure S20: Long Serial Interval Scenario: A) Correlation between the number of ZIKV
cases by state in Colombia as reported by surveillance data through October 1, 2016 [27],
compared with state-level model projections of infections (median with 95% CI). Pearson’s r
correlation coefficient is reported for the linear association on the log scale. The outlier (in dark
green) excluded from the statistical analysis corresponds to the Arauca region. B) Timeline
of microcephaly cases in Brazil though April 30, 2016. Bar plot shows weekly definite (or
highly probable cases) and moderately (or somewhat probable cases) from surveillance data
[28]. Line plots indicate estimated weekly new microcephaly cases given three levels of first
trimester risk: 4.52% (round) [26], 2.19% (square) [26], and 0.95% (diamond) [21]. C) Bar plot of
ZIKV infections imported into the continental USA by state(s) as reported by CDC surveillance
through October 5, 2016 [29], and compared to model projections (median with 95% CI) for
the same period assuming 5.74% reporting/detection. The insert shows the correlation between
CDC surveillance data and model projections (median with 95% CI).
30

7 Counterfactual seasonality scenarios
To illustrate how seasonality a↵ects Zika epidemic in terms of both local transmission and
global dissemination, we create two counterfactual scenarios with unrealistic seasonal patterns
and we compare the ZIKV transmission dynamics with the reference scenario that instead uses
real-world seasonality pattern. The detailed settings of the two counterfactual scenarios are as
follows:
•Counterfactual Scenario One (CS1): we set the daily temperature pattern of the
entire Brazil to be the same as Sao Paulo (Brazil), in which the temperature variation
throughout the year significantly limits ZIKV transmission feasibility during winter. The
rest of the world maintains its original temperature pattern. This is a lower-bound scenario
that illustrates how unsuitable climate in Brazil limits ZIKV epidemics in the Americas in
terms of both timing and magnitude of the epidemic. All the other elements of the model
are otherwise kept the same as in the Reference Scenario (RS) detailed in the main article.
•Counterfactual Scenario Two (CS2): the daily temperature pattern of the entire world
is set to be the same as Fortaleza (Brazil), whose tropical climate allows ZIKV transmission
all year long. This is an upper-bound scenario to illustrate how suitable climate facilitate
the spread of Zika, providing unrealistic patterns when compared to reported data. All
the other elements of the model are otherwise kept the same as in the Reference Scenario
(RS) detailed in the main article.
For each counterfactual scenario, a total of 15,000 simulations were performed with the time
of introduction in Brazil on November 15, 2013 (in agreement with phylogenetic studies and
posterior estimation of the RS) and seeding locations as in the reference scenario. Figure S21
shows the cumulative number of ZIKV infections per 1000 people in Brazil for CS1, CS2 and
RS. Here we consider only simulations with outbreaks in Brazil (>1000 cases total in Brazil).
CS1 (lower bound scenario, red color in figure) has a slower growth rate at the beginning of the
epidemic, and a much lower overall attack rate when compared to the RS. CS2 (upper bound
scenario, yellow color in figure), in contrast, has a large growth rate at the beginning of the
epidemic and higher overall country attack rate. This is in agreement with the climate settings
of the two hypothetical scenarios.
31

Figure S21: Conterfactual scenarios: cumulative number of ZIKV infections per 1000 people
in Brazil for CS1, CS2 and RS
32

8 Additional validation tests
In this section, we provide additional model validation tests based on surveillance data of travel
associated ZIKV cases among European countries [30] and state level microcephaly cases in
Brazil [31].
Figure S22 shows the correlation between the number of imported ZIKV infections from
model projection (reference scenario) and reported travel-associated ZIKV cases from ECDC
surveillance by November 2016. The Pearson correlation coefficient is r=0.89 (p<0.01),
indicating that numerical results are in good agreement with observations.
Figure S23 shows the correlation of the model-projected number of births with first trimester
ZIKV infections and the number of suspected and confirmed microcephaly cases from surveil-
lance data of di↵erent states in Brazil. Based on the model projection, birth defects related to
Zika have the highest concentration in Northeast region of Brazil, followed by Southeast, North,
Central-West, and South. This is in agreement with the spatial distribution of microcephaly
cases observed throughout Brazil.
Figure S22: Travel associated ZIKV cases: Correlation between imported ZIKV infections
(median with 95% CI) projected by model and travel-associated ZIKV cases reported by ECDC
surveillance, through November, 2016[30]. Countries with reported travel-associated ZIKV cases
includes Austria, Belgium, Czech Republic, Denmark, Finland, France, Greece, Hungary, Ire-
land, Italy, Luxembourg, Malta, the Netherlands, Norway, Portugal, Romania, Spain, Sweden,
the United Kingdom.
33

Figure S23: Microcephaly cases in Brazil: Correlation of cumulative suspected and con-
firmed microcephaly cases by state in Brazil as reported by surveillance data [31] through
November 19, 2016, compared with state-level model projections of births with first trimester
ZIKV infections (median with 95% CI) during the same time window.
9 Incidence map of ZIKV infections
In Figure S24 we provide a spatial projection of the cumulative median number of ZIKV in-
fections, according to the reference scenario, by February 28, 2017 at a spatial resolution of
1⇥1km in Latin America and the Caribbean. Each 1 ⇥1km cell is colored according to the
median number of ZIKV infections within the cell. It worth noticing the close similarity of our
spatial projection with the analogous map obtained by Perkins et al.[11] by using a di↵erent
methodology.
34

Figure S24: Incidence map of ZIKV infections: A spatial projection (reference scenario) of
median number of ZIKV infections by February 28, 2017 at a spatial resolution of 1 ⇥1km in
Latin America and the Caribbean. In the insets A) and B) we provide detailed projections fro
the areas of Recife and Belo Horizonte, Brazil, respectively.
35

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