带有病毒携带猪和环境病毒的非洲猪瘟传染病模型的稳定性分析与最优控制

王坤; 张瑞霞

doi:10.6040/j.issn.1671-9352.0.2024.214

山东大学学报(理学版) ›› 2026, Vol. 61 ›› Issue (2) : 64 -74. DOI: 10.6040/j.issn.1671-9352.0.2024.214

带有病毒携带猪和环境病毒的非洲猪瘟传染病模型的稳定性分析与最优控制

王坤 ,
张瑞霞 ^*

作者信息 +

Stability analysis and optimal control of the epidemic model with virus-carrier and environmental virus for African swine fever

Kun WANG ,
Ruixia ZHANG ^*

Author information +

文章历史 +

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摘要

为研究病毒携带猪和环境中病毒对非洲猪瘟(African swine fever， ASF)传播的影响，建立非洲猪瘟传播模型，运用下一代矩阵法计算基本再生数 R₀，讨论平衡点的存在性，分析无病平衡点和地方病平衡点的局部稳定性和全局稳定性。应用庞特里亚金(Pontryagin)极大值原理和最优控制理论得出最优控制解。最后，数值模拟验证理论的正确性，并揭示病毒携带猪和环境中的病毒对传播的影响。最优控制模拟结果表明，在有控制的情况下，感染数量有所减少。

Abstract

To investigate the impact of virus-carrying pigs and environmental viruses on the spread of African swine fever (ASF), an ASF transmission model is constructed. The basic reproduction number R₀ is calculated by the next generation matrix method. The existence of the equilibrium point is discussed, and the local stability and global stability of the disease-free equilibrium and the endemic equilibrium are analyzed. By applying Pontryagin’s maximum principle and optimal control theory, the optimal control solution is obtained. Finally, the numerical simulations verify the correctness of the conclusion and reveal the influence of the virus carrying pigs and the virus in the environment on the transmission. The optimal control simulation results show that the number of infections is reduced under controlled conditions.

关键词

非洲猪瘟 / 传染病模型 / 基本再生数 / 稳定性 / 最优控制

Key words

African swine fever / epidemic model / basic reproduction number / stability / optimal control

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