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A free boundary problem of a diffusive SIRS model with nonlinear incidence

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Abstract

This paper is concerned with the spreading (persistence) and vanishing (extinction) of a disease which is characterized by a diffusive SIRS model with a bilinear incidence rate and free boundary. Through discussing the dynamics of a free boundary problem of an SIRS model, the spreading of a disease is described. We get the sufficient conditions which ensure the disease spreading or vanishing. In addition, the estimate of the expanding speed is also given when the free boundaries extend to the whole \(\mathbb {R}\).

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Authors and Affiliations

  1. School of Mathematics and Statistics, Lanzhou University, Lanzhou, 730000, Gansu, People’s Republic of China

    Jia-Feng Cao, Wan-Tong Li, Jie Wang & Fei-Ying Yang

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  1. Jia-Feng Cao
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  2. Wan-Tong Li
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  3. Jie Wang
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  4. Fei-Ying Yang
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Correspondence to Wan-Tong Li.

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Cao, JF., Li, WT., Wang, J. et al. A free boundary problem of a diffusive SIRS model with nonlinear incidence. Z. Angew. Math. Phys. 68, 39 (2017). https://doi.org/10.1007/s00033-017-0786-8

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  • DOI: https://doi.org/10.1007/s00033-017-0786-8

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