A time-periodic dengue fever model in a heterogeneous environment.

The transmission of dengue fever characterizes seasonality and periodicity, in particular, the infection of dengue fever is more serious during the warmer seasons. In this paper, we formulate and study an SIS–SI dengue model associated with the spatial heterogeneity and temporal periodicity. With the help of the spectral radius of next infection operator and eigenvalue problem, we introduce the basic reproduction number R0 of the dengue model. Furthermore, the existence and nonexistence of the positive T-periodic solution are obtained, respectively. The asymptotical stability of T-periodic solution is also investigated. Our analyses reveal that the combination of spatial heterogeneity and temporal periodicity would enhance the persistence of dengue virus in the case of R0>1. Some theoretical results are illustrated by the final numerical simulations and epidemiological explanations.