The authors have declared that no competing interests exist.
Dengue, chikungunya, and Zika virus epidemics transmitted by
Mosquitoborne viruses like dengue, Zika, and chikungunya have recently caused large epidemics that are partly driven by temperature. Using a mathematical model built from laboratory experimental data for
Over the last 30–40 years, arboviral outbreaks have dominated the public health landscape globally [
Informed public health decisions to limit the spread and magnitude of these arboviral epidemics depend on a robust understanding of transmission dynamics. One mechanistic modeling framework, the Susceptible–Infected–Recovered (SIR) model, has been implemented successfully to model the dynamics of outbreaks of influenza, measles, and vectorborne diseases such as CHIKV and ZIKV [
Arbovirus dynamics are strikingly seasonal and geographically restricted to relatively warm climates [
Here, we expand on previous work with three main advances: (1) we incorporate the full suite of empiricallyderived, unimodal thermal responses for all known transmissionrelevant mosquito and parasite traits; (2) we examine the influence of seasonal temperature mean and variation (in contrast to constant temperatures or daily temperature variation); and (3) we use a dynamic transmission framework to explore the impact of different seasonal temperature regimes on the epidemiologicallyrelevant outcomes of epidemic size, duration, and peak incidence (in contrast to R_{0}, or vectorial capacity, which are difficult to measure directly). To do so, we incorporate previously estimated and independently validated thermal response functions for all vector and parasite traits [
We adopted an SEISEIR compartmental modeling framework to simulate arboviral transmission by the
The SEI portion of the model describes the vector population, where
Traits were fit to a Brière [
Trait  Definition  Function  Fitted Parameters  

Biting rate (day^{1})  Brière  
Eggs laid per female per day  Brière  
Probability of mosquito eggtoadult survival  Quadratic  
Mosquito eggtoadult development rate (day^{1})  Brière  
Adult mosquito lifespan (days)  Quadratic  
Probability of mosquito infectiousness  Brière  
Probability of mosquito infection  Brière  
Virus extrinsic incubation rate (day^{1})  Brière 
The SEIR portion of the model describes the human population, where
Parameter  Definition  Value  Source 

Intrinsic incubation period (days)  5.9  [ 

Human infectivity period (days)  5.0  [ 

Proportion of initially infectious humans  0.0001  
Proportion of initially infectious mosquitoes  0.015  [ 

Ratio of mosquitoestohumans at 29°C  2.0  [ 
Since the lifespan of an adult mosquito is short relative to the timespan of an epidemic, we allowed mosquito birth and death rates to drive population dynamics. Additionally, the birth rate of susceptible mosquitoes was regulated by a temperaturedependent carrying capacity,
Here,
We included a temperaturedependent carrying capacity in the model to constrain the growth of the mosquito population. As described in the Appendix, all simulations begin with the mosquito population at its (temperaturedependent) carrying capacity. As the temperature changes seasonally, the mosquito population does not necessarily remain at carrying capacity if one or more of the life history traits that determine the production of new mosquitoes in Eq (
It should be noted that the transmission parameters are only related to the current temperature at each time point in the simulation. Time lags for each life history trait were not explicitly built into the model.
To address seasonality in the model, we allowed temperature to vary over time. We modeled temperature as a sinusoidal curve with a period of 365 days of the form:
To incorporate seasonal forcing into the compartmental modeling framework, we used fitted mechanistic thermal response curves [
Mordecai et al. [
To identify areas of epidemic suitability across the globe, we extracted monthly mean temperatures for 2016 from Weather Underground (
Monthly mean temperatures during 2016 were extracted from Weather Underground.
City  Annual Mean Temperature (°C)  Annual Temperature Amplitude (°C) 

Buenos Aires, Argentina  16.5  8.0 
Sao Paulo, Brazil  20.6  5.0 
Rio de Janeiro, Brazil  24.3  4.0 
Salvador, Brazil  26.3  2.0 
Fortaleza, Brazil  27.8  0.50 
Belo Horizonte, Brazil  21.9  3.0 
Recife, Brazil  27.2  1.5 
Shanghai, China  17.6  12.5 
Beijing, China  12.8  16 
Guangzhou, China  22.9  8.0 
Bogotá, Colombia  14.7  1.0 
Medellin, Colombia  17.9  1.0 
Cali, Colombia  25.1  1.5 
Barranquilla, Colombia  28.8  1.0 
Cartagena, Colombia  28.6  1.0 
Delhi, India  26.3  9.5 
Tokyo, Japan  17.0  10.5 
Kobe, Japan  17.4  11 
Manila, Philippines  29.0  1.5 
New York, USA  13.8  12 
We first examined how epidemic dynamics varied across different constant temperatures. Here, we did not introduce seasonal forcing into the model but rather assumed static life history traits for
Using the model that included seasonal variation in temperature, we examined how the dynamics of an epidemic varied due to the temperature at which the epidemic began, under two temperature regimes. First, we set
Using the compartmental modeling framework with the default starting conditions, we examined the variation in final epidemic size as a result of seasonal forcing. To do so, we simulated over a wide range of temperature mean and seasonal variance regimes. The mean annual temperature varied from 10.0°C to 38.0°C in increments of 0.1°C, while the seasonal variation about the mean (i.e.,
To observe the interaction of population immunity with the seasonal temperature regime, we simulated the model assuming that 0, 20, 40, 60, or 80% of the population was initially immune. Each simulation began with the introduction of the infected individual occurring at the mean seasonal temperature.
We then compared simulated climate regimes with actual climates in major cities, to measure relative epidemic suitability of the following cities: São Paulo, Brazil; Rio de Janeiro, Brazil; Salvador, Brazil; Fortaleza, Brazil; Belo Horizonte, Brazil; Recife, Brazil; Bogotá, Colombia; Medellín, Colombia; Cali, Colombia; Barranquilla, Colombia; Cartagena, Colombia; Tokyo, Japan; Delhi, India; Manila, Philippines; Shanghai, China; Beijing, China; New York City, USA; Guangzhou, China; Kobe, Japan; and Buenos Aires, Argentina, given 0, 20, 40, 60, and 80% population immunity. These cities were chosen because they represent some of the most populous urban areas across South America and throughout the world.
To characterize uncertainty in the model, we sampled 50 joint posterior estimates for
Holding temperature constant, we examined variability in epidemic dynamics across four temperatures: 20°C, 25°C, 30°C, and 35°C. As temperature increased from 20°C to 30°C, the number of susceptible individuals depleted more rapidly (
The model was simulated under default parameters at four constant temperatures: 20°C, 25°C, 30°C, and 35°C.
Next, we examined variability in epidemic dynamics due to the temperature at which the epidemic began, given two seasonal temperature regimes (25°C mean and a seasonal range of 10°C to 40°C or 20°C to 30°C, respectively). Given that an epidemic occurred, epidemic length monotonically decreased as a function of starting temperature for the first temperature regime (
The red curve represents the maximum number of humans in the infected class (
In contrast to epidemic length, the response of final epidemic size and maximum number of infected individuals to the temperature at epidemic onset depended on the amount of seasonal temperature variation. When temperature varied widely, from 10°C to 40°C, both final epidemic size and the maximum number of infected individuals responded unimodally to starting temperature, with peaks at 23.9°C and 24.1°C, respectively (
To address how mean temperature and seasonal variance combined to influence the final epidemic size, we simulated over a wide range of temperature regimes that accounted for variation in the mean and temperature range over a calendar year. We calculated relative epidemic suitability, defined as the final epidemic size as a proportion of the human population, for twenty major cities worldwide (
Epidemic suitability was calculated as the proportion of the population that became infected in simulations run with 0, 20, 40, 60, or 80% initial population immunity. Temperature at simulation onset was set to the mean of the temperature regime. Each city was simulated with its respective temperature regime from the 2016 calendar year.
Epidemic Suitability  

City  0% Immunity  20% Immunity  40% Immunity  60% Immunity  80% Immunity 
Buenos Aires, Argentina  0.03656  0.02169  0.01203  0.005975  0.002295 
Sao Paulo, Brazil  0.6056  0.3386  0.1518  0.05351  0.01385 
Rio de Janeiro, Brazil  0.9984  0.7962  0.5891  0.3618  0.09862 
Salvador, Brazil  0.9990  0.7976  0.5937  0.3804  0.1335 
Fortaleza, Brazil  0.9993  0.7982  0.5953  0.3861  0.1535 
Belo Horizonte, Brazil  0.5909  0.3344  0.1544  0.05771  0.01633 
Recife, Brazil  0.9994  0.7985  0.5959  0.3871  0.1517 
Shanghai, China  0.9966  0.7878  0.5507  0.2484  0.03456 
Beijing, China  0.5268  0.2526  0.09058  0.02298  0.003587 
Guangzhou, China  0.9996  0.7989  0.5965  0.3848  0.1254 
Bogotá, Colombia  0.0001000  0.0001000  0.0001000  0.0001000  0.0001000 
Medellin, Colombia  0.002544  0.002048  0.001556  0.001068  0.0005820 
Cali, Colombia  0.9909  0.7822  0.5617  0.3122  0.07217 
Barranquilla, Colombia  0.9997  0.7993  0.5979  0.3928  0.1703 
Cartagena, Colombia  0.9997  0.7993  0.5978  0.3923  0.1688 
Delhi, India  0.9537  0.7215  0.4759  0.2388  0.06803 
Tokyo, Japan  0.7269  0.4149  0.1758  0.05159  0.009489 
Kobe, Japan  0.9435  0.6669  0.3522  0.1090  0.01632 
Manila, Philippines  0.9998  0.7994  0.5981  0.3933  0.1720 
New York, USA  0.04088  0.02159  0.01041  0.004390  0.001425 
In a lowvariation thermal environment, a band of mean temperatures between approximately 25°C and 35°C supports the highest epidemic suitability (
The heat map shows the epidemic suitability (represented as the proportion of the total human population infected during an epidemic) as a function of mean annual temperature and temperature range. Here, temperature range is defined as the seasonal variation about the annual mean temperature. Twenty large, globally important cities are plotted to illustrate their epidemic suitability.
Of the focal 20 major cities, those with high mean temperature and small average temperature variation exhibited the highest epidemic suitability. For instance, Manila, Philippines, which has a monthly mean temperature of 29°C and average seasonal amplitude in mean temperature of 1.50°C, had an epidemic suitability of 0.9998. Cartagena and Barranquilla, Colombia had epidemic suitability of 0.9997. On the other hand, areas with low average temperature and greater temperature variation, such as Beijing and New York, exhibited lower—but still nonzero—epidemic suitabilities of 0.5268 and 0.04088 respectively. Notably, Guangzhou and Shanghai, China have high epidemic suitability (0.9996 and 0.9966, respectively) despite moderate mean temperatures (22.9 and 17.6°C, respectively) due to high seasonal variation in temperature. By contrast, high seasonal variation reduced suitability to 0.9537 in Delhi, India, which has a high mean temperature of 26.3°C (
The relationship between epidemic suitability and seasonal temperature regime was consistent across varying levels of population immunity. Locations with high mean temperatures and small average temperature variation had higher epidemic suitability, regardless of the level of population immunity (
Epidemic suitability also varied by starting temperature, depending on the seasonal temperature regime. The epidemic suitability of cities with high mean temperature and small average temperature variation—such as Manila, Philippines and Cartagena and Barranquilla, Colombia—did not depend on starting temperature (
The heat map shows the epidemic suitability (represented as the proportion of the total human population infected during an epidemic) as a function of mean annual temperature and temperature range averaged across simulations where the initial temperature was set to the seasonal temperature regime’s minimum, mean, or maximum temperature. Here, temperature range is defined as the seasonal variation about the annual mean temperature. Twenty large, globally important cities are plotted to illustrate their epidemic suitability.
Epidemic suitability was calculated as the proportion of the population that became infected in simulations that began at the minimum, mean, or maximum temperature of the seasonal temperature regime. Each city was simulated with its respective temperature regime from the 2016 calendar year with 0% population immunity.
Epidemic Suitability  

City  Minimum Starting Temperature  Mean Starting Temperature  Maximum Starting Temperature  
Buenos Aires, Argentina  0.0001000  0.03656  0.1166  
Sao Paulo, Brazil  0.02026  0.6056  0.3480  
Rio de Janeiro, Brazil  0.9978  0.9984  0.9760  
Salvador, Brazil  0.9965  0.9990  0.9963  
Fortaleza, Brazil  0.9986  0.9993  0.9990  
Belo Horizonte, Brazil  0.09404  0.5909  0.3273  
Recife, Brazil  0.9973  0.9994  0.9987  
Shanghai, China  0.0001000  0.9966  0.8905  
Beijing, China  0.0001000  0.5268  0.5792  
Guangzhou, China  0.9983  0.9996  0.9912  
Bogotá, Colombia  0.0001000  0.0001000  0.0001000  
Medellin, Colombia  0.0002177  0.002544  0.004472  
Cali, Colombia  0.9858  0.9909  0.9623  
Barranquilla, Colombia  0.9994  0.9997  0.9997  
Cartagena, Colombia  0.9993  0.9997  0.9997  
Delhi, India  0.5615  0.9537  0.6954  
Tokyo, Japan  0.0001000  0.7269  0.5121  
Kobe, Japan  0.0001000  0.9435  0.6890  
Manila, Philippines  0.9994  0.9998  0.9998  
New York, USA  0.0001000  0.04088  0.1863 
Estimated epidemic suitability is close to one in the most suitable temperature regimes because we assumed that: (i) the population was fully susceptible at the start of the epidemic; (ii) mixing was homogeneous among humans and mosquitoes; (iii) all cases of infection are included regardless of whether or not they are symptomatic; and (iv) no other environmental or social drivers are limiting transmission. As a result, the epidemic suitability metric should be considered an upper bound on the proportion of the population that could become infected based on temperature alone.
Final epidemic size was not sensitive to life history trait parameterization (
There was uncertainty in the specific numerical values of the epidemiological indices across starting temperatures (
Recent outbreaks of DENV, CHIKV, and ZIKV in Latin America and across the globe have captured the attention of the public health community and underscore the importance of preparation for future outbreaks. As temperatures rise, the global landscape suitable for such outbreaks will expand and shift geographically, potentially placing a larger proportion of the world’s population at risk [
At constant temperature, epidemics varied substantially in the rate at which susceptible individuals were depleted. Epidemics simulated at 25°C and 30°C reached similar sizes but the epidemic at 25°C proceeded at a much slower rate (
The temperature at which an epidemic started affected dynamics only under large ranges of temperature variation. When temperature ranged from 10°C to 40°C, the final epidemic size peaked at intermediate starting temperatures (24°C;
At mean starting temperatures, epidemic suitability was sensitive to the interaction between annual temperature mean and seasonal variation. Under low seasonal temperature variation, a narrow band of annual mean temperatures (approximately 25–35°C) had the highest epidemic suitability (Figs
The relationship between epidemic suitability and the seasonal temperature regime also depended on the temperature at the epidemic onset. Three distinct relationships emerged (Figs
With rising mean annual temperatures and increasing seasonal temperature variation due to climate change, the landscape of epidemic suitability is likely to shift. Importantly, areas with previously low epidemic suitability may have increasing potential for transmission yearround. By contrast, warming temperatures may drive epidemics in cities with high current suitability (e.g., Manila, Philippines, Barranquilla, Colombia, and Fortaleza, Brazil) to shift toward cooler months. Thus, climate change may alter not only epidemic size and duration but also seasonal timing globally, as it interacts with other important drivers like rainfall and human behavior.
It is important to note that modelestimated epidemic suitability should be treated as an upper bound on the potential for large epidemics because within highly suitable climate regimes, epidemics can vary in magnitude due to human population size and movement dynamics [
Although seasonal temperature dynamics provide insight into vectorborne transmission dynamics, other factors like mosquito abundance, vector control, and rainfall also determine transmission dynamics. Thus, temperature must be considered jointly with these factors. Moreover, accurately describing epidemic dynamics of emerging and established vectorborne pathogens will ultimately require integrating realistic models of environmental suitability, as presented here, with demographic, social, and economic factors that promote or limit disease transmission [
The red curve represents the median maximum number of humans in the infected class (
(TIF)
The heat map shows the epidemic suitability (represented as the proportion of the total human population infected during an epidemic) as a function of mean annual temperature and temperature range assuming 20% population immunity. Here, temperature range is defined as the seasonal variation about the annual mean temperature. Twenty large, globally important cities are plotted to illustrate their epidemic suitability.
(TIF)
The heat map shows the epidemic suitability (represented as the proportion of the total human population infected during an epidemic) as a function of mean annual temperature and temperature range assuming 40% population immunity. Here, temperature range is defined as the seasonal variation about the annual mean temperature. Twenty large, globally important cities are plotted to illustrate their epidemic suitability.
(TIF)
The heat map shows the epidemic suitability (represented as the proportion of the total human population infected during an epidemic) as a function of mean annual temperature and temperature range assuming 60% population immunity. Here, temperature range is defined as the seasonal variation about the annual mean temperature. Twenty large, globally important cities are plotted to illustrate their epidemic suitability.
(TIF)
The heat map shows the epidemic suitability (represented as the proportion of the total human population infected during an epidemic) as a function of mean annual temperature and temperature range assuming 80% population immunity. Here, temperature range is defined as the seasonal variation about the annual mean temperature. Twenty large, globally important cities are plotted to illustrate their epidemic suitability.
(TIF)
The heat map shows the epidemic suitability (represented as the proportion of the total human population infected during an epidemic) as a function of mean annual temperature and temperature range. Here, temperature range is defined as the seasonal variation about the annual mean temperature, and the simulation began at the minimum temperature of the regime. Twenty large, globally important cities are plotted to illustrate their epidemic suitability.
(TIF)
The heat map shows the epidemic suitability (represented as the proportion of the total human population infected during an epidemic) as a function of mean annual temperature and temperature range. Here, temperature range is defined as the seasonal variation about the annual mean temperature, and the simulation began at the maximum temperature of the regime. Twenty large, globally important cities are plotted to illustrate their epidemic suitability.
(TIF)
Epidemic suitability (represented as the proportion of the total human population infected during an epidemic) as a function of mean annual temperature and the temperature range. Temperature varied according to a seasonal temperature regime, and 50 samples of c, T_{min}, and T_{max} were taken from the joint posterior distribution of each trait thermal response from Mordecai et al. [
(TIF)
Epidemic suitability (represented as the proportion of the total human population infected during an epidemic) as mean annual temperature and the temperature range. Temperature varied according to a seasonal temperature regime, and 50 samples of c, T_{min}, and T_{max} were taken from the joint posterior distribution of each trait thermal response from Mordecai et al. [
(TIF)
Epidemic suitability (represented as the proportion of the total human population infected during an epidemic) as mean annual temperature and the temperature range. Temperature varied according to a seasonal temperature regime, and 50 samples of c, T_{min}, and T_{max} were taken from the joint posterior distribution of each trait thermal response from Mordecai et al. [
(TIF)
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