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 910 and show that 910 is a threshold parameter: if 910 <= 1, then the disease-free equilibrium is globally asymptotically stable; if 910 > 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 910, 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 910. Particularly, we find that spatial heterogeneity may increase the risk of disease transmission.(c) 2022 Elsevier Inc. All rights reserved.

Automated summary

In this paper, a degenerate dengue fever model with distinct dispersal rates in heterogeneous environment is proposed. The well-posedness of the model and the existence of the global attractor are obtained. The basic reproduction number 910 is defined as a threshold parameter: if 910 <= 1, the disease-free equilibrium is globally asymptotically stable; if 910 > 1, the system is uniformly persistent, and the endemic equilibrium is globally attractive when the spatial environment is homogeneous. The impact of the dispersal rate on disease transmission is shown through studying the asymptotic profiles of the positive steady state and 910. Numerical simulations are conducted to illustrate the effect of model parameters on 910, and it is found that spatial heterogeneity may increase the risk of disease transmission. (c) 2022 Elsevier Inc. All rights reserved.