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A SIS reaction-diffusion model with a free boundary condition and nonhomogeneous coefficients

  • * Corresponding author: S. Guo

    * Corresponding author: S. Guo
The second author is supported by NSF of China (Grants No. 11671123).
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  • This paper is devoted to a spatial heterogeneous SIS model with the infected group equipped with a free boundary. Our main aim is to determine whether the disease is spreading forever or extinct eventually, and to illustrate, under the nonhomogeneous spatial environment, free boundaries can have a large influence on the infected behavior at the large time. For this purpose, we first introduce a basic reproduction number and then establish a spreading-vanishing dichotomy. Then by investigating the effect of the diffusion rate, initial domain and spreading speed on the asymptotic behavior of the infected group, we establish some sufficient conditions and even necessary and sufficient conditions for disease spreading or vanishing.

    Mathematics Subject Classification: Primary: 35K57, 92D30; Secondary: 35R35, 35J47.


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