### Mathematical Biosciences and Engineering

2017, Issue 5&6: 1071-1089. doi: 10.3934/mbe.2017056

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

• Received: 01 July 2016 Accepted: 01 October 2016 Published: 01 October 2017
• MSC : Primary: 35B36, 45M10; Secondary: 92C15

• 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 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 low-risk habitat for the population to effectively control the spread of the epidemic disease. This may provide some potential applications in disease control.

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

### Related Papers:

• 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 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 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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