A dynamics analysis of an SIS epidemic reaction-diffusion model with treatment

Abstract

In this paper, we study the SIS epidemic reaction-diffusion model with the saturated treatment. We obtain the prevalence threshold value of disease, namely the basic reproduction number R0, based on the least eigenvalue. We have proved that the unique disease-free equilibrium is local stable when R0<1, while the disease-free equilibrium is unstable and the endemic equilibrium exists when R0>1. Through numerical simulation, we discuss the influence of treatment on prevalence of disease. When disease outbreaks, it is efficient to increase cure rate for the control of the disease, while expanding the scale of hospitals will cause even more prevalence of the disease.

Keywords

• differential dynamic system
• SIS epidemic reaction-diffusion model
• treatment
• basic reproduction number
• disease-free equilibrium
• endemic equilibrium