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A reaction–diffusion SIS epidemic model in an almost periodic environment

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Abstract

A susceptible–infected–susceptible almost periodic reaction–diffusion epidemic model is studied by means of establishing the theories and properties of the basic reproduction ratio \({R_{0}}\). Particularly, the asymptotic behaviors of \({R_{0}}\) with respect to the diffusion rate \({D_{I}}\) of the infected individuals are obtained. Furthermore, the uniform persistence, extinction and global attractivity are presented in terms of \({R_{0}}\). Our results indicate that the interaction of spatial heterogeneity and temporal almost periodicity tends to enhance the persistence of the disease.

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Authors and Affiliations

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

    Bin-Guo Wang, Wan-Tong Li & Zhi-Cheng Wang

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  1. Bin-Guo Wang
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  2. Wan-Tong Li
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  3. Zhi-Cheng Wang
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Correspondence to Bin-Guo Wang.

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Wang, BG., Li, WT. & Wang, ZC. A reaction–diffusion SIS epidemic model in an almost periodic environment. Z. Angew. Math. Phys. 66, 3085–3108 (2015). https://doi.org/10.1007/s00033-015-0585-z

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  • DOI: https://doi.org/10.1007/s00033-015-0585-z

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