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The authors have declared that no competing interests exist.

Recent epidemics of Zika, dengue, and chikungunya have heightened the need to understand the seasonal and geographic range of transmission by

Understanding the drivers of recent Zika, dengue, and chikungunya epidemics is a major public health priority. Temperature may play an important role because it affects virus transmission by mosquitoes, through its effects on mosquito development, survival, reproduction, and biting rates as well as the rate at which mosquitoes acquire and transmit viruses. Here, we measure the impact of temperature on transmission by two of the most common mosquito vector species for these viruses,

Epidemics of dengue, chikungunya, and Zika are sweeping through the Americas, and are part of a global public health crisis that places an estimated 3.9 billion people in 120 countries at risk [

Predicting transmission of DENV, CHIKV, and ZIKV requires understanding the ecology of the vector species. For these viruses the main vector is

The effects of temperature on ectotherms are largely predictable from fundamental metabolic and ecological processes. Survival, feeding, development, and reproductive rates predictably respond to temperature across a variety of ectotherms, including mosquitoes [

We synthesize available data to characterize the temperature-dependent traits of the mosquitoes and viruses that determine transmission intensity. With these thermal responses, we develop mechanistic temperature-dependent virus transmission models for

Data gathered from the literature [

Informative priors based on data from additional

We estimated the posterior distribution of _{0}(

Solid lines: mean posterior estimates; dashed lines: 95% credible intervals. _{0} curves normalized to a 0–1 scale for ease of comparison and visualization.

The posterior distribution of _{0}(

We used generalized linear models (GLM) to ask whether the predicted relationship between temperature and transmission, _{0}(_{0}(_{0}(_{0}(_{0}(_{0}(_{0}) and the log of population size (_{0}. (Here, and throughout, _{0}(_{0}(_{0}(_{0}(_{0}(_{0}(_{0}(

For the probability of autochthonous transmission occurring, the model that included both the _{0}(_{0}(_{0}(_{0}(_{0}(_{0} from population size, so for simplicity we show the model predictors that combines _{0} and population size here (see Table D in _{0}(_{0}(

A, _{0} (the posterior probability that _{0}(_{0}(_{0}(_{0} or _{0}(_{0} and _{0}(

_{0}(_{0}(_{0}(_{0}(_{0}(_{0}(_{0}(

Although predicted _{0}(

The ability of the model to explain the probability and magnitude of transmission is notable given the coarse scale of the human incidence versus mean temperature data (i.e., country-scale means), the lack of CHIKV- and ZIKV-specific trait thermal response data to inform the model, the nonlinear relationship between transmission and incidence, and all the well-documented factors other than temperature that influence transmission. Together, these analyses show simple mechanistic models parameterized with laboratory data on mosquitoes and dengue virus are consistent with observed temperature suitability for transmission. Moreover, the similar responses of human incidence of ZIKV, CHIKV, and DENV to temperature suggest that the thermal ecology of their shared mosquito vectors is a key determinant of outbreak location, timing, and intensity.

The validated model can be used to predict where transmission is not excluded (posterior probability that _{0}(_{0}(_{0} > 0), ranging from the most to least conservative (Fig D in

Color indicates the consecutive months in which temperature is permissive for transmission (predicted _{0} > 0) for _{0} > 0). Black lines indicate the CDC estimated range for the two

Temperature is an important driver of—and limitation on—vector transmission, so accurately describing the temperature range and optimum for transmission of DENV, CHIKV, and ZIKV is critical for predicting their geographic and seasonal patterns of spread [

Mechanistic understanding is valuable for extrapolating beyond the current spatial and temporal range of transmission (

Even though the thermal response data are imperfect—for example, CHIKV and ZIKV thermal response data are missing—and the human case data are reported at a coarse spatial scale, the validation analyses suggest that _{0}(

Predicting arbovirus transmission at a higher spatial resolution and precision will require more detailed information on factors like the exposure and susceptibility of human populations, environmental variation (e.g., oviposition habitat availability, seasonal and daily temperature variation), and socioeconomic factors. However, as a first step our mechanistic model provides valuable insight because it makes broad predictions about suitable environmental conditions for transmission, it is mechanistic and grounded in experimental trait data, it is validated against independent human case data, and its predictions are applicable across three different viruses. Using these thermal response models as a scaffold, additional drivers could be incorporated to obtain more precise and specific predictions about transmission dynamics, which could in turn be used for public health and vector control applications. For this purpose, all code and data used in the models are available on Figshare [

The socio-ecological conditions that enabled CHIKV, ZIKV, and DENV to become the three most important emerging vector-borne diseases in the Americas make the emergence of additional

We constructed temperature-dependent models of transmission using a previously developed _{0} framework. We modeled transmission rate as the basic reproduction rate, _{0}—the number of secondary infections that would originate from a single infected individual introduced to a fully susceptible population. In previous work on malaria, we adapted a commonly used expression for _{0} for vector transmission to include the temperature-sensitive traits that drive mosquito population density [

Here, (_{EA} is the mosquito egg-to-adult survival probability, _{0})(_{m})) or asymmetric (Brière, _{0})(_{m}^{1/2}) unimodal thermal response models to the available empirical data [_{0} and _{m} are respectively the minimum and maximum temperature for transmission, and

We consider a normalized version of the _{0} equation such that it is rescaled to range from zero to one with the value of one occurring at the unimodal peak. Although absolute values of _{0} that are used to determine when transmission is stable depend on additional factors not captured in our model, the minimum and maximum temperatures for which _{0} > 0 map exactly onto our normalized equations, allowing us to accurately calculate whether or not transmission should be possible at all. Empirical estimates of absolute values of _{0} are difficult to obtain in any case, but it is much easier to determine whether transmission is occurring and for how long. While different model formulations for predicting _{0} versus temperature can produce results with different magnitudes and potentially different overall shapes [_{0} is above or below zero (or one) are mostly model independent. For instance, two competing models differ only by whether or not the formula in Eq (_{0} value) greater than one is always greater than one, and the square of a number less than one is always less than one. Therefore, the threshold temperatures at which absolute _{0} > 0 or absolute _{0} > 1 will be exactly the same for either choice of formula (Fig F in _{0}, including the square of Eq (_{0} adequately describes the nonlinear relationship between mosquito and virus traits and transmission.

We fit the trait thermal responses in Eq (

Following Johnson _{0} ~ Uniform (0, 24), _{m} ~ Uniform (25, 45), _{0} < _{m} and we assumed that temperatures below 0°C and above 45°C were lethal). Any negative values for all thermal response functions were truncated at zero, and thermal responses for probabilities (_{EA}, _{0} from 15–40°C, producing a posterior distribution of _{0} versus temperature. We summarized the relationship between temperature and each trait or overall _{0} by calculating the mean and 95% highest posterior density interval (HPD interval; a type of credible interval that includes the smallest continuous range containing 95% of the probability, as implemented in the

We fit a second set of models for each mosquito species that used informative priors to reduce uncertainty in _{0} versus temperature and in the trait thermal responses. In these models, we used Gamma-distributed priors for each parameter _{0}, _{m}, _{0}, _{m}, and

Because organisms do not typically experience constant temperature environments in nature, we incorporated the effects of temperature variation on transmission by calculating a daily average _{0} assuming a daily temperature range of 8°C, across the range of mean temperatures. This range is consistent with daily temperature variation in tropical and subtropical environments but lower than in most temperate environments. At each mean temperature, we used a Parton-Logan model to generate hourly temperatures and calculate each temperature-sensitive trait on an hourly basis [_{m} in Tables A-B in _{0} across a range of mean temperatures. We used this model in the validation against human cases (

To validate the model, we used data on human cases of DENV, CHIKV, and ZIKV at the country scale and mean temperature during the transmission window. Using statistical models (as described below), we estimated the effects of predicted _{0}(

We matched the DENV, CHIKV, and ZIKV incidence data with temperature using daily temperature data from METAR stations in each country, averaged at the country level by epidemic week. A previous study found a six-week lagged relationship between temperature and oviposition for

We accessed available data on projected 2016 gross domestic product (GDP) for countries of interest via the International Monetary Fund’s World Economic Outlook Database (

To validate the _{0}(

We were interested in understanding whether _{0}(_{0}(_{0}(_{0}, which is the posterior probability that _{0}(_{0}, where _{0}-based predictor for the PA analysis. For the incidence analysis, we instead use _{0}(_{0}(

In both the PA and incidence analyses, we first used the full data sets to examine which of the candidate models best described the data. Randomized quantile residuals indicated that the logistic and gamma GLM models were performing adequately. We compared the approximate model probabilities, calculated from the BIC scores, as well as the proportion of deviance explained (D^{2}) from each model. Next we examined the performance of the models in predicting out of sample, for both PA and incidence analyses. To do this we created 1000 random partitions, where 90% of the data were used to train the model and 10% were used for testing. In the PA analyses we classified each partition based on presence/absence, with separate classification thresholds for DENV versus CHIKV/ZIKV as these grouping had much different probabilities of occurrence. We assessed the performance of the model for the PA analysis based on the mean misclassification rate. In the incidence analyses we assessed the model performance based on the predictive mean absolute percentage error (MAPE). Since differences in prediction success between the models in both the PA and incidence analyses were not statistically significant, we present the simpler models that only include the _{0}(_{0}(

The residuals of the incidence model exhibit “inverse trumpeting,” in which residual variation is larger at low than high predicted incidence (Fig I in _{0}(

Using the validated model, we were interested in where the temperature was suitable for _{0} models for both mosquitoes. We calculated the number of consecutive months in which the posterior probability of _{0} > 0 exceeds a threshold of 0.025, 0.5, or 0.975 for both mosquito species, representing the maximum, median, and minimum likely ranges, respectively. The minimum range is shown in _{0} > 0 exceeded the threshold at the temperatures in those cells. We then synthesized the monthly grids into a single raster that reflected the maximum number of consecutive months where cell values equaled one. The resulting rasters were plotted in ArcGIS 10.3, overlaying the three cutoffs (Fig D in

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Barry Alto, Krijn Paaijmans, Francis Ezeakacha, and Helene Delatte kindly provided raw data used in the analyses. We gratefully acknowledge the Centers for Disease Control and Prevention Epidemic Predictions Initiative (CDC EPI) for collating and sharing the Zika incidence data on GitHub (