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

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.