JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2022, Vol. 57 ›› Issue (11): 70-77.doi: 10.6040/j.issn.1671-9352.0.2021.452

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Dynamics of a spatially heterogeneous SI epidemic model with nonlocal diffusion

JIAO Zhan1, JIN Zhen2*   

  1. 1. Complex System Research Center, Shanxi University, Taiyuan 030006, Shanxi, China;
    2. Shanxi Key Laboratory of Mathematical Technology and Big Data Analysis on Disease Control and Prevention, Shanxi University, Taiyuan 030006, Shanxi, China
  • Published:2022-11-10

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Abstract: We study a spatially heterogeneous non-local dispersal SI epidemic model with the standard incidence. The basic reproduction number R0 of the system is defined as the spectral radius of the next generation operator, and by means of suitable Lyapunov functional, the global asymptotic stability of the disease-free equilibrium is proved when R0<1; the upper and lower solutions are used to prove the existence, uniqueness and global asymptotic stability of the endemic equilibrium of the system when the dispersal rate DS=0 of susceptible individuals and R0>1.

Key words: SI epidemic model, nonlocal diffusion, standard incidence, global asymptotic stability

CLC Number: 

  • O175.5
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