一类具有性别结构的SIQR传染病模型的动力学分析
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重庆师范大学 数学科学学院

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Dynamics Analysis of a SIQR Epidemic Model with sex-structured
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College of Mathematical Sciences,Chongqing Normal University

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    【目的】对一类感染男女比率不同的传染病模型做动力学行为分析。【方法】首先验证模型的正定性和有界性;其次通过再生矩阵法计算传染病模型的基本再生数,即传染病最终是否消亡的阈值;然后利用Hurwitz判据讨论平衡点的局部稳定性;最后构造Lyapunov泛函,通过LaSalle不变集原理得到全局渐近稳定的阈值条件。【结果】研究结果为无病平衡点在基本再生数小于1时局部稳定且全局渐近稳定,基本再生数大于1时存在唯一的正平衡点,该点局部稳定且全局渐近稳定。【结论】该研究拓展了与性别结构有关的传染病动力学模型的内容。

    Abstract:

    [Purposes]The dynamics of a class of infectious disease models with varying male-to-female infection ratios were analyzed. [Methods]Initially, the positivity and boundedness of the model were validated, followed by the computation of the basic reproduction number using the regeneration matrix method to determine the threshold for disease extinction. Subsequently, the local stability of equilibrium points was discussed using the Hurwitz criterion. Finally, a Lyapunov functional was constructed, and the threshold conditions for global asymptotic stability were obtained through the LaSalle invariant set principle. [Findings] The research results show that the disease-free equilibrium point is locally stable and globally asymptotically stable when the basic reproduction number is less than 1, and there is a unique positive equilibrium point when the basic reproduction number is greater than 1, which is locally stable and globally asymptotically stable.[Conclusions] This study extends the content of infectious disease dynamics models related to sex-structures.

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  • 收稿日期:2024-04-23
  • 最后修改日期:2024-08-18
  • 录用日期:2025-02-24
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