Global dynamics and asymptotic profiles for a degenerate Dengue fever model in heterogeneous environment

Abstract

In this paper, we propose a degenerate dengue fever model with distinct dispersal rates in heterogeneous environment. Firstly, we obtain the well-posedness of the model and the existence of the global attractor. Secondly, we define the basic reproduction number ℜ0 and show that ℜ0 is a threshold parameter: if ℜ0≤1, then the disease-free equilibrium is globally asymptotically stable; if ℜ0>1, the system is uniformly persistent, and the endemic equilibrium is globally attractive when the spatial environment is homogeneous. Thirdly, by studying the asymptotic profiles of the positive steady state and ℜ0, we show the impact of the dispersal rate on disease transmission. We conclude with some numerical simulations to illustrate the effect of some model parameters on ℜ0. Particularly, we find that spatial heterogeneity may increase the risk of disease transmission.