On a Diffusive Susceptible-Infected-Susceptible Epidemic Model with Mass Action Mechanism and Birth-Death Effect: Analysis, Simulations, and Comparison with Other Mechanisms

In the present paper, we are concerned with a susceptible-infected-susceptible epidemic reaction-diffusion model governed by a mass action infection mechanism and linear birth-death growth with no flux boundary condition. By performing qualitative analysis, we study the stability of the disease-free equilibrium, uniform persistence property in terms of the basic reproduction number and the global stability of the endemic equilibrium in a homogeneous environment, and investigate the asymptotic profile of endemic equilibria (when they exist) in a heterogeneous environment when the movement rate of the susceptible and infected populations is small. Our results, together with those in previous works on three other closely related modeling systems, suggest that factors such as infection mechanism, variation of total population, and population movement play vital but subtle roles in the transmission dynamics of diseases and hence provide useful insights into the strategies designed for disease control and prevention.