This project will develop mathematical models to study the dynamics of Zika virus introduced to southern Florida. The investigators will carry out mathematical, statistical and computational analyses of these models to better understand factors affecting the geographical spread of Zika. Several vector-borne diseases (VBDs), such as dengue, chikungunya and Zika, have been imported into Florida, caused local outbreaks (dengue in 2009-2010 and 2013, chikungunya in 2014, Zika in 2016), and posed major public health problems. Dengue, chikungunya and Zika share the same primary mosquito vectors, Aedes aegypti and Aedes albopictus, both abundant in Florida and capable of transmitting several other diseases. The transmission cycle of these VBDs is heavily influenced by seasonal changes, climate conditions, and human movement. Based on data from 2016 Zika outbreaks in Miami Beach, Wynwood, and Little River in Florida, they will build and calibrate models including the age structure of both hosts and vectors as well as the effects of seasonality to study the spatial and temporal dynamics and spread of Zika in Florida. The objectives are to be better prepared to anticipate and respond to similar reemerging arboviruses such as dengue, chikungunya and yellow fever viruses. The project involves graduate students and postdoctoral trainees and results will be disseminated through seminars, conference presentations and journal publications.
The goals of this project are: (i) Since dengue, chikungunya and Zika viruses have significant agreement in their spatiotemporal distributions, the PIs will develop a multi-scale (multi-region) multi-patch model to study the geographical spread of VBD. A large scale is used to describe the long distance human movement from regions to regions and a small scale is used to model the short distance movement of both mosquitoes and humans from patches to patches within a region. The model will be applied to simulate the geographical and local spread of Zika among Miami Beach, Wynwood, and Little River in 2016 and will be studied employing multiple scale analysis and slow-fast dynamical system theory. (ii) Since age distributions of both vectors and hosts are very important in the spread of VBD, the PIs will construct age-structured models to study the effect of age distributions of both mosquitoes and humans on the transmission of VBD and use the model to design optimal vector control policies and to access disease risk for different age groups. (iii) Since age-structured models can be written as abstract equations in Banach spaces and seasonality imposes a natural temporal period, the PIs will study the nonlinear dynamics of semilinear periodic equations and apply the results to age-structured VBD models with seasonal change. Studying the nonlinear dynamics of periodic solutions in the semilinear periodic Cauchy problem will be transformative since the results will be useful in studying periodic delay equation models, time-periodic reaction-diffusion equations, and age-structured periodic models arising from biology and epidemiology.
This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.
