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《山东大学学报(理学版)》 ›› 2022, Vol. 57 ›› Issue (11): 70-77.doi: 10.6040/j.issn.1671-9352.0.2021.452

• • 上一篇    

空间异质的非局部扩散SI传染病模型的动力学

焦战1,靳祯2*   

  1. 1.山西大学复杂系统研究所, 山西 太原 030006;2.山西大学疾病防控的数学技术与大数据分析山西省重点实验室, 山西 太原 030006
  • 发布日期:2022-11-10
  • 作者简介:焦战(1997— ),男,硕士研究生,研究方向为生物数学、复杂网络. E-mail:jiaozhan0215@163.com*通信作者简介:靳祯(1965— ),男,博士,教授,研究方向为生物数学、复杂网络. E-mail:jinzhn@263.net
  • 基金资助:
    国家自然科学基金资助项目(61873154)

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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摘要： 研究了具有标准发生率的空间异质性非局部扩散SI传染病模型。利用下一代算子的谱半径方法计算了系统的基本再生数R0,借助Lyapunov函数证明了R0<1时无病稳态解的全局渐近稳定性;当易感者的扩散率DS=0且R0>1时,利用上、下解等方法证明了系统地方病稳态解的存在性、唯一性与全局渐近稳定性。

关键词: SI传染病模型, 非局部扩散, 标准发生率, 全局渐近稳定性

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

中图分类号: 

  • O175.5
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