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Qualitative analysis on a spatial SIS epidemic model with linear source in advective environments: I standard incidence

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Abstract

This paper is concerned with a reaction–diffusion SIS epidemic model with standard incidence infection mechanism and linear source in advective heterogeneous environments. We have derived the threshold-type dynamics in terms of the basic reproduction number \({\mathcal {R}}_0\): the disease will be eliminated if \({\mathcal {R}}_0\le 1\) while it persists uniformly if \({\mathcal {R}}_0>1\). The global asymptotic stability of the endemic equilibrium is discussed in a special case. We mainly investigate the effects of linear source, advection and diffusion on asymptotic profiles of the endemic equilibrium. It is shown that the linear source can enhance persistence of infectious disease, advection may induce the concentration phenomenon and small dispersal rate of infected individuals can eradicate the disease. These results may offer some implications on disease control and prediction.

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Acknowledgements

The authors thank the anonymous reviewers for careful reading and helpful comments which improved the initial manuscript. R Cui is the corresponding author and supported by National Natural Science Foundation of China (No. 12171125) and Natural Science Foundation of Heilongjiang Province (No. LH2020A012). X Chen is supported by Postgraduate Innovation Project of Harbin Normal University (No. HSDSSCX2021-11).

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  1. Y.Y.Tseng Functional Analysis Research Center and School of Mathematical Sciences, Harbin Normal University, Harbin, 150025, Heilongjiang, People’s Republic of China

    Xiaodan Chen & Renhao Cui

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  1. Xiaodan Chen
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  2. Renhao Cui
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Correspondence to Renhao Cui.

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Chen, X., Cui, R. Qualitative analysis on a spatial SIS epidemic model with linear source in advective environments: I standard incidence. Z. Angew. Math. Phys. 73, 150 (2022). https://doi.org/10.1007/s00033-022-01795-9

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  • DOI: https://doi.org/10.1007/s00033-022-01795-9

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