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

Bao Xiang Zhang; Yong Li Cai; Bing Xian Wang; Wei Ming Wang

doi:10.3934/mbe.2020047

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

Math Biosci Eng. 2019 Nov 6;17(1):893-909. doi: 10.3934/mbe.2020047.

Authors

Bao Xiang Zhang¹, Yong Li Cai¹, Bing Xian Wang¹, Wei Ming Wang¹

Affiliation

¹ School of Mathematics and Statistics, Huaiyin Normal University, Huaian, 223300, China.

PMID: 31731383
DOI: 10.3934/mbe.2020047

Abstract

This paper performs qualitative analysis on a reaction-diffusion SIRS epidemic system with ratio-dependent incidence rate in spatially heterogeneous environment. The threshold dynamics in the term of the basic reproduction number R₀ 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.

Keywords: asymptotic profile; basic reproduction number; ratio–dependent incidence rate; spatial heterogeneity; threshold dynamics.

Publication types

Research Support, Non-U.S. Gov't

MeSH terms

Algorithms
Basic Reproduction Number*
Communicable Disease Control*
Communicable Diseases / epidemiology
Disease Susceptibility / epidemiology
Epidemics*
Humans
Incidence
Models, Biological
Stochastic Processes