Qualitative analysis on a spatial SIS epidemic model with linear source in advective environments II saturated incidence

TL;DR

This paper analyzes a spatial SIS epidemic model with saturated incidence and linear source, examining stability, effects of diffusion and advection, and conditions for disease eradication or persistence.

Contribution

It provides a comprehensive qualitative analysis of the model, including stability criteria and the impact of parameters like advection, saturation, and linear source on disease dynamics.

Findings

Advection can cause concentration phenomena in disease spread.

Small dispersal rates of infected individuals may lead to disease eradication.

Large saturation levels can accelerate disease elimination.

Abstract

In this paper, we consider a reaction-diffusion-advection SIS epidemic model with saturated incidence rate and linear source. We study the uniform bounds of parabolic system and some asymptotic behavior of the basic reproduction number $\mathcal{R}_0$, according to which the threshold-type dynamics are given. Furthermore, we show the globally asymptotic stability of the endemic equilibrium in a special case with a large saturated incidence rate. Meanwhile, we investigate the effects of diffusion, advection, saturation and linear source on the asymptotic profiles of the endemic equilibrium. Our study shows that advection may induce the concentration phenomenon and the disease will be eradicated with small dispersal rate of infected individuals. Moreover, our results also reveal that the linear source can enhance persistence of infectious disease and large saturation can help speed up the elimination of disease.