Global Dynamics of a Reaction-Diffusion Model of Zika Virus Transmission with Seasonality

In this paper, we propose a periodic reaction-diffusion model of Zika virus with seasonal and spatial heterogeneous structure in host and vector population. We introduce the basic reproduction ratio R-0 for this model and show that the disease-free periodic solution is globally asymptotically stable if R-0 <= 1, while the system admits a globally asymptotically stable positive periodic solution if R-0>1. Numerically, we study the Zika transmission in Rio de Janeiro Municipality, Brazil, and investigate the effects of some model parameters on R-0. We find that the neglect of seasonality underestimates the value of R-0 and the maximum carrying capacity affects the spread of Zika virus.