### Mathematical Biosciences and Engineering

2020, Issue 1: 893-909. doi: 10.3934/mbe.2020047
Research article Special Issues

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

• 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.

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

### Related Papers:

• 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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