A spatial SIS model in heterogeneous environments with vary advective rate

Xiaowei An; Xianfa Song; Xiaowei An; Xianfa Song

doi:10.3934/mbe.2021276

Mathematical Biosciences and Engineering

2021, Volume 18, Issue 5: 5449-5477. doi: 10.3934/mbe.2021276

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Research article

A spatial SIS model in heterogeneous environments with vary advective rate

Xiaowei An ¹,
Xianfa Song ^{2
,
,}

1.
School of Intelligence Policing, China People's Police University, Langfang, He Bei, 065000, China
2.
Department of Mathematics, School of Mathematics, Tianjin University, Tianjin, 300072, China

Received: 31 March 2021 Accepted: 25 May 2021 Published: 18 June 2021

We study a spatial susceptible-infected-susceptible(SIS) model in heterogeneous environments with vary advective rate. We establish the asymptotic stability of the unique disease-free equilibrium(DFE) when $ \mathcal{R}_0 < 1 $ and the existence of the endemic equilibrium when $ \mathcal{R}_0 > 1 $. Here $ \mathcal{R}_0 $ is the basic reproduction number. We also discuss the effect of diffusion on the stability of the DFE.
- spatial SIS model,
- vary advective rate,
- disease-free equilibrium,
- endemic equilibrium
Citation: Xiaowei An, Xianfa Song. A spatial SIS model in heterogeneous environments with vary advective rate[J]. Mathematical Biosciences and Engineering, 2021, 18(5): 5449-5477. doi: 10.3934/mbe.2021276

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Abstract

We study a spatial susceptible-infected-susceptible(SIS) model in heterogeneous environments with vary advective rate. We establish the asymptotic stability of the unique disease-free equilibrium(DFE) when $ \mathcal{R}_0 < 1 $ and the existence of the endemic equilibrium when $ \mathcal{R}_0 > 1 $. Here $ \mathcal{R}_0 $ is the basic reproduction number. We also discuss the effect of diffusion on the stability of the DFE.

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