Spatial dynamics of a diffusive SIRI model with distinct dispersal rates and heterogeneous environment

Lian Duan; Lihong Huang; Chuangxia Huang

doi:10.3934/cpaa.2021120

Article Contents

2021, Volume 20, Issue 10: 3539-3560. Doi: 10.3934/cpaa.2021120 open access

This issue Previous Article Regular attractors of asymptotically autonomous stochastic 3D Brinkman-Forchheimer equations with delays Next Article Global well-posedness of the Navier-Stokes equations with Navier-slip boundary conditions in a strip domain

Spatial dynamics of a diffusive SIRI model with distinct dispersal rates and heterogeneous environment

1.
School of Mathematics and Big Data, Anhui University of Science and Technology, Huainan 232001, Anhui, China
2.
School of Computer Engineering and Applied Mathematics, Changsha University, Changsha 410022, Hunan, China
3.
School of Mathematics and Statistics, Changsha University of Science and Technology, Changsha 410114, Hunan, China

^* Corresponding author
^* Corresponding author

Received: January 2021

Revised: June 2021

Early access: July 2021

Published: October 2021

This work was jointly supported by the Major Program of University Natural Science Research Fund of Anhui Province(KJ2020ZD32), Anhui Provincial Natural Science Foundation (1808085QA01), China Postdoctoral Science Foundation (2018M640579), Anhui Provincial Postdoctoral Science Foundation (2019B329), and National Natural Science Foundation of China (11701007, 11771059, 1197107)

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Abstract

In this paper, we are concerned with the dynamics of a diffusive SIRI epidemic model with heterogeneous parameters and distinct dispersal rates for the susceptible and infected individuals. We first establish the basic properties of solutions to the model, and then identify the basic reproduction number $ \mathscr{R}_{0} $ which serves as a threshold parameter that predicts whether epidemics will persist or become globally extinct. Moreover, we study the asymptotic profiles of the positive steady state as the dispersal rate of the susceptible or infected individuals approaches zero. Our analytical results reveal that the epidemics can be extinct by limiting the movement of the susceptible individuals, and the infected individuals concentrate on certain points in some circumstances when limiting their mobility.

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Mathematics Subject Classification: Primary: 35B35, 35K57; Secondary: 37N25.

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