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

Baoxiang Zhang; Yongli Cai; Bingxian Wang; Weiming Wang

doi:10.3934/mbe.2020047

Mathematical Biosciences and Engineering, 2020, 17(1): 893-909. doi: 10.3934/mbe.2020047. Research article Special Issues

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

Baoxiang Zhang, Yongli Cai, Bingxian Wang, Weiming Wang

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

Received: , Accepted: , Published:

Special Issues: Spatial dynamics for epidemic models with dispersal of organisms and heterogenity of environment

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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.

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Keywords: 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. Mathematical Biosciences and Engineering, 2020, 17(1): 893-909. doi: 10.3934/mbe.2020047

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