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Mathematical Biosciences and Engineering (MBE)
 

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

Pages: 1071 - 1089, Volume 14, Issue 5/6, October/December 2017      doi:10.3934/mbe.2017056

 
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Yongli Cai - School of Mathematical Science, Huaiyin Normal University, Huaian 223300, China (email)
Yun Kang - Science and Mathematics Faculty, School of Letters and Sciences, Arizona State University, Mesa, AZ 85212, United States (email)
Weiming Wang - School of Mathematical Science, Huaiyin Normal University, Huaian 223300, China (email)

Abstract: 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 reproductoin 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.

Keywords:  Basic reproduction number, disease-free equilibrium, endemic, spatial heterogeneity.
Mathematics Subject Classification:  Primary: 35B36, 45M10; Secondary: 92C15.

Received: July 2016;      Accepted: October 2016;      Available Online: May 2017.

 References