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

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    * Corresponding author 
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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  • 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.

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


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