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The authors have declared that no competing interests exist.

Conceived and designed the experiments: DRM ISV KEO LCH. Performed the experiments: DRM ISV KEO. Analyzed the data: DRM. Contributed reagents/materials/analysis tools: DRM ISV KEO. Wrote the paper: DRM LCH. Designed the software used in analysis: DRM.

Chikungunya is a mosquito-borne viral infection of humans that previously was confined to regions in central Africa. However, during this century, the virus has shown surprising potential for geographic expansion as it invaded other countries including more temperate regions. With no vaccine and no specific treatment, the main control strategy for Chikungunya remains preventive control of mosquito populations. In consideration for the risk of Chikungunya introduction to the US, we developed a model for disease introduction based on virus introduction by one individual. Our study combines a climate-based mosquito population dynamics stochastic model with an epidemiological model to identify temporal windows that have epidemic risk. We ran this model with temperature data from different locations to study the geographic sensitivity of epidemic potential. We found that in locations with marked seasonal variation in temperature there also was a season of epidemic risk matching the period of the year in which mosquito populations survive and grow. In these locations controlling mosquito population sizes might be an efficient strategy. But, in other locations where the temperature supports mosquito development all year the epidemic risk is high and (practically) constant. In these locations, mosquito population control alone might not be an efficient disease control strategy and other approaches should be implemented to complement it. Our results strongly suggest that, in the event of an introduction and establishment of Chikungunya in the US, endemic and epidemic regions would emerge initially, primarily defined by environmental factors controlling annual mosquito population cycles. These regions should be identified to plan different intervention measures. In addition, reducing vector: human ratios can lower the probability and magnitude of outbreaks for regions with strong seasonal temperature patterns. This is the first model to consider Chikungunya risk in the US and can be applied to other vector borne diseases.

Chikungunya fever is a mosquito-borne viral infection showing a surprising potential for geographic expansion. Similar to other tropical infectious diseases having no vaccine and no specific treatment, the main control strategy for Chikungunya remains reduction of mosquito population size. We developed a model for disease introduction that combines a climate based mosquito population dynamics stochastic model with an epidemiological model in order to identify temporal windows during which disease introduction through one exposed individual might compromise the health status of the entire human population. We ran this model with temperature data from different locations showing the geographic sensitivity of this risk. The identification of temporal windows with epidemic risk at different spatial locations is key to guiding mosquito population control campaigns. Locations with marked seasonal variation also have a season with high epidemic risk matching the period in which mosquito populations survive and grow, therefore controlling mosquito population sizes might be an optimal strategy in those areas. However, locations with other temperature patterns may need additional control strategies to avoid epidemics. To our knowledge, this is the first model to explore Chikungunya introduction in the USA. Our modeling approach can be used for other vector borne diseases and can be expanded to compare the outcome with different control strategies.

Chikungunya fever (CHIKF) is a mosquito-borne viral infection first isolated in Tanzania in 1953

The onset of the symptoms occurs after an intrinsic incubation period in the human host of approximately 4 days post infection

Laboratory studies have demonstrated that CHIKV disseminates to the salivary glands in competent mosquitoes quickly, within 2 days (range 1–14 days) post-infection

The Asian tiger mosquito,

Several laboratory studies on

Concerns for the role of

In this study, we explicitly evaluated the risk of epidemic events by simulating the introduction of Chikungunya virus into three naïve US populations. Assuming established mosquito populations in each area, we introduced one exposed individual to evaluate the epidemic potential size of an outbreak, taking into account the population dynamics of the vector and its susceptibility to temperature regimes. We predicted low epidemic risk for disease introduction during periods of low vector abundance and high epidemic risk for certain critical periods that show increasing, or high, vector abundance. These results provide valuable additional information not only for early warning systems but also for the implementation of intervention strategies with the goal of reducing vector populations or human risk of exposure.

To study the dynamics of the introduction of CHIKV in an immunologically naive population we constructed a model with demographic stochasticity for mosquitoes and humans (^{S}), asymptomatic infective (I^{A}) and recovered (R) classes. Analogously, the adult mosquito population was divided into susceptible (S), exposed (E) and infected (I) classes. In addition, we considered the immature stages of mosquito population, including mosquito eggs (G), larvae and pupae (L) and eggs undergoing diapause (D). Vital mosquito rates in this model were temperature dependent (

Squares (circles) represent the dynamic model for humans (mosquitoes). Human population is divided into susceptible (S), exposed (E), symptomatic (I^{S}) and asymptomatic (I^{A}) infective, and recovered (R) individuals. Mosquito population is divided into immature eggs (G), larvae (L) and eggs under a diapause (D) state, and mature susceptible (S), exposed (E) and infected (I) states. Full arrows represent transition from one state to the other. Lines with parallel end represent natural mortality. Dotted lines represent infection dynamics. A full description of the parameters and the model can be found in Material S1.

Panels with full lines represent functional shapes based on assumptions, those with dotted lines are functional shapes fitted to data (points). See Material S1 for a full mathematical representation of these functions.

The functional forms of the temperature forcing on the parameters for the dynamic of the vector population are presented in _{sD} and T_{eD}) were used to determine the diapause state. Eggs entered diapause (i.e., arrested development) when temperature was below T_{sD}, and eggs do not undergo diapause for temperatures above T_{eD}. The proportion of eggs undergoing (avoiding) the diapause state linearly decreased (increased) with increasing temperature for environmental conditions between T_{sD} and T_{eD}. Although the determination of diapause periods follows a complex combination of factors — including temperature and photoperiod— temperature was used as a proxy for such combination in here. Dependence on temperature of both egg survival and development time was fitted to experimental data (Harrington, unpublished data) and reports from the literature

Daily temperatures were calculated by applying a spline interpolation to the monthly mean temperature data of the last decade obtained from the Intergovernmental Panel on Climate Change (

Population sizes and carrying capacity parameters for human populations were estimated using the city size data reported in the last census (

The model was run for five years. Initial population sizes in the model were selected according to the expected equilibrium values. During the first year of simulation there was no disease present in the model and therefore both human and mosquito populations drifted to their respective equilibria. CHIKV was introduced into the model during the second year of simulation via one exposed individual, and the simulation was run until the end of the fifth year. We calculated the final number of infective individuals, the number of infected at the outbreak peak, and the time to reach the outbreak peak from the day of introduction for each one of 1000 Monte Carlo simulations. We ran the simulations systematically varying the day of introduction of the disease from January 1st to December 31st, which allowed us to express the outbreak probability as a function of the introduction day (

Probability of outbreak (left y-axes) as a function of day of introduction of CHIKV (x-axes) with a ratio of vector to hosts equals to 0.5 and 100% for meal preference. Full dark lines represent the mean of 1000 Monte Carlo simulations. Gray areas represent the standard deviation. Dotted lines are temperature values for the different locations (right y-axes). See Material S1 for other parameter combinations.

Proportion of infected individuals (left y-axes) as a function of day of introduction of CHIKV (x-axes) with a ratio of vector to host equals to 0.5 and 100% for meal preference. Notice different panels have different left y-axes limits. Full dark lines represent the mean of 1000 Monte Carlo simulations. Gray areas represent the standard deviation. Dotted lines are temperature values for the different locations (right y-axes). See Material S1 for other parameter combinations.

^{th} to September 11^{th}. In addition, there is a significant probability of outbreak after an introduction on June 15^{th} and up to December. The probability of having an outbreak late in November is very small and it is a consequence of using mean monthly temperature data as a basis for the temperature patterns.

Outbreaks also were seasonal for Atlanta, with no significant probability of outbreaks after introductions between January 12^{th} and April 9^{th}. Moreover, in Atlanta, the probability of outbreak was greater than 30% for a longer period, extending from June 6^{th} to September 26^{th}, with peak values similar to those in New York. In contrast, for Miami chances of a CHIKV outbreak were significant after an introduction at any time during the year.

Our model only demonstrated the occurrence of at least one successful transmission event, however, the maximum prevalence reached for those outbreaks is likely to be a more important parameter (

Additionally, we calculated the number of days from pathogen introduction until the peak prevalence (

Meal Preference | |||

Vector/Host Ratio | 25% | 100% | |

New York | 0.5 | 4.960 (4.62–5.06) | 9.759 (4.64–10.11) |

1 | 5.277 (4.61–5.39) | 14.732 (4.66–16.71) | |

3 | 7.080 (4.63–7.43) | 23.514 (4.70–35.62) | |

Atlanta | 0.5 | 5.146 (4.67–5.55) | 21.182 (4.89–37.32) |

1 | 5.772 (4.73–6.84) | 45.704 (5.11–80.92) | |

3 | 10.458 (4.84–17.32) | 55.390 (5.92–74.56) | |

Miami | 0.5 | 5.655 (5.35–5.93) | 87.719 (77.34–97.48) |

1 | 7.006 (6.43–7.51) | 88.723 (84.77–92.34) | |

3 | 35.520 (26.87–42.72) | 73.876 (72.66–75.24) |

Since the occurrence of the CHIKF outbreak in Italy in 2007, the risk of similar outbreaks in the United States and other temperate countries has become a public health concern

Our model outputs display higher sensitivity to parameters controlling the proportion of blood meals from humans than the vector: host ratio. Nevertheless, the increased ratio of mosquitoes to humans led to a two-fold increase in the probability of outbreak at all locations. This result highlights the importance of vector control to reduce both the risk of outbreaks and the proportion of infected individuals. It is important to note that, in this modeling approach, both parameters may be interpreted as proxies for a reduction of human exposure to mosquitoes. Hence, our results confirm the relevance of public campaigns advising residents to control mosquitoes at home and take precautions to avoid mosquito exposure to reduce disease outbreaks.

The time between CHIKV introduction and peak outbreaks revealed that, for locations with temperature patterns similar to those of Miami where mosquito populations may not undergo diapause, CHIKV infections might circulate at low levels for several months until reaching dramatic proportions. Early detection of cases in these regions will be important to reduce the magnitude of an outbreak. However, in locations such as New York and Atlanta, a critical temporal window for interventions could be identified and intervention during such periods may be enough to significantly reduce the probability of an outbreak.

It is clear that these predictive models are highly sensitive to temperature patterns that govern mosquito population dynamics, and could be improved by using non-averaged temperature data (i.e. sampling from the distribution of temperatures), and including other environmental factors such as rainfall and photoperiod that can have a significant influence on vector populations. In addition, reduction of individual exposure (only modeled as a reduction in human feeding patterns here) should be considered in order to have more accurate predictions. This modeling approach highlights the fact that a better understanding of epidemiological dynamics will require further studies on both biological and non-biological processes. Especially important will be: (1) further studies on diapause, abundance and feeding biology of

Our results strongly suggest that, in the event of an introduction and establishment of CHIKV in the United States, endemic and epidemic regions would emerge initially, mainly defined by environmental factors controlling annual mosquito population cycles. These regions should be identified in order to plan different intervention measures. In addition, reducing mosquito population sizes (and, consequently, reducing vector: human ratios) can lower the probability and magnitude of outbreaks mainly for regions with strongly marked seasonal temperature patterns.

Typical control strategies for vector borne diseases are: (1) reduction of vector population, (2) reduction of host exposure to infectious mosquito bites, and (3) isolation of infective hosts. This model also allows for evaluation of the effects of changes in the mosquito feeding patterns. Simulation results suggest that a reduction of vector population and human exposure could be very effective for a reduction of both the risk of an outbreak and the population at risk.

The results presented here simulating significant CHIK outbreaks in the US were based on a conservative approach of one exposed individual introduced to a region

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