Global stability of the steady states of an epidemic model incorporating intervention strategies

In this paper, we investigate the global stability of the steady states of a general reaction-diffusion epidemiological model with infection force under intervention strategies in a spatially heterogeneous environment.We prove that the reproduction number $mathcal{R}_0$ can be played an essential role in determining whether the disease will extinct or persist: if $mathcal{R}_0 lt 1$ , there is Nails a unique disease-free equilibrium which is globally asymptotically stable; and if $mathcal{R}_0 gt 1$ , there exists a unique endemic equilibrium which is globally asymptotically stable.Furthermore, we study the relation between $mathcal{R}_0$ with the diffusion and spatial heterogeneity and find that, it seems very necessary to create a garden candle low-risk habitat for the population to effectively control the spread of the epidemic disease.This may provide some potential applications in disease control.