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

1. School of Mathematical Science, Huaiyin Normal University, Huaian 223300, China
2. Sciences and Mathematics Faculty, College of Integrative Sciences and Arts, Arizona State University, Mesa, AZ 85212, USA

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 $\mathcal{R}_0<1 there="" is="" a="" unique="" disease-free="" equilibrium="" which="" is="" globally="" asymptotically="" stable="" and="" if="" mathcal="" r="" _0="">1$, 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 low-risk habitat for the population to effectively control the spread of the epidemic disease. This may provide some potential applications in disease control.

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Keywords Basic reproduction number; disease-free equilibrium; endemic; spatial heterogeneity

Citation: Yongli Cai, Yun Kang, Weiming Wang. Global stability of the steady states of an epidemic model incorporating intervention strategies. Mathematical Biosciences and Engineering, 2017, 14(5&6): 1071-1089. doi: 10.3934/mbe.2017056


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