Dynamics and asymptotic profiles of steady states of an SIRS epidemic model in spatially heterogenous environment

Baoxiang Zhang; Yongli Cai; Bingxian Wang; Weiming Wang; Baoxiang Zhang; Yongli Cai; Bingxian Wang; Weiming Wang

doi:10.3934/mbe.2020047

Mathematical Biosciences and Engineering

2020, Volume 17, Issue 1: 893-909. doi: 10.3934/mbe.2020047

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Dynamics and asymptotic profiles of steady states of an SIRS epidemic model in spatially heterogenous environment

School of Mathematics and Statistics, Huaiyin Normal University, Huaian, 223300, China

Received: 11 August 2019 Accepted: 24 October 2019 Published: 06 November 2019

This paper performs qualitative analysis on a reactionɃdiffusion SIRS epidemic system with ratioɃdependent incidence rate in spatially heterogeneous environment. The threshold dynamics in the term of the basic reproduction number $\mathcal{R}_{0}$ is established. And the asymptotic profile of endemic equilibrium is determined if the diffusion rate of the susceptible individuals is small. The results show that restricting the movement of susceptible individuals can effectively control the number of infectious individuals.
- ratio–dependent incidence rate,
- spatial heterogeneity,
- basic reproduction number,
- threshold dynamics,
- asymptotic profile
Citation: Baoxiang Zhang, Yongli Cai, Bingxian Wang, Weiming Wang. Dynamics and asymptotic profiles of steady states of an SIRS epidemic model in spatially heterogenous environment[J]. Mathematical Biosciences and Engineering, 2020, 17(1): 893-909. doi: 10.3934/mbe.2020047

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Abstract

This paper performs qualitative analysis on a reactionɃdiffusion SIRS epidemic system with ratioɃdependent incidence rate in spatially heterogeneous environment. The threshold dynamics in the term of the basic reproduction number $\mathcal{R}_{0}$ is established. And the asymptotic profile of endemic equilibrium is determined if the diffusion rate of the susceptible individuals is small. The results show that restricting the movement of susceptible individuals can effectively control the number of infectious individuals.

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