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 R₀ can be played an essential role in determining whether the disease will extinct or persist: if R₀ < 1, there is a unique disease-free equilibrium which is globally asymptotically stable; and if R₀ > 1, there exists a unique endemic equilibrium which is globally asymptotically stable. Furthermore, we study the relation between R₀ with the diffusion and spatial heterogeneity and find that, it seems very necessary to create a low-risk habitat for the population to effectively control the spread of the epidemic disease. This may provide some potential applications in disease control.