一类具有饱和发生率的分数阶SIVS传染病模型的稳定性分析  

Stability Analysis of a Fractional-Order SIVS Epidemic Model with Saturated Incidence Rate

作　　者：胡行华[1] 刘盈月 HU Xing-hua;LIU Ying-yue(College of Science,Liaoning Technical University,Fuxin 123000,China)

机构地区：[1]辽宁工程技术大学理学院,辽宁阜新123000

出　　处：《数学的实践与认识》2024年第10期109-120,共12页Mathematics in Practice and Theory

基　　金：教育部人文社科规划基金(21YJCZH204);辽宁省社科学规划基金(L22BGL028);辽宁省社科联规划基金(2022lslwtkt-069)。

摘　　要：构建一类考虑感染差异性及饱和发生率的Caputo分数阶SIVS传染病模型,计算模型的无病平衡点和基本再生数,确定地方病平衡点的存在唯一性,利用分数阶矩阵特征值方法与Routh-Hurwitz准则判定两个平衡点的局部渐近稳定性,构造Lyapunov函数并使用分数阶Barbalat引理获得两个平衡点全局渐近稳定的充分条件.最后,通过不同分数阶次的数值模拟验证理论结果的正确性,并发现分数阶模型数值解拥有更大的自由度.此模型中饱和常数增大所反映的易感者保护措施的增强可有效缓解疾病传播.In this paper,we construct a Caputo fractional-order SIvS epidemic model with infection difference and the saturated incidence rate.The disease-free equilibrium point and the basic reproduction number of the model are calculated,and the existence and uniqueness of the endemic equilibrium point are determined.The local asymptotic stability of the two equilibrium points is determined by using the fractional matrix eigenvalue method and the Routh-Hurwitz criterion.The suficient conditions for the global asymptotic stability of two equilibrium points are obtained by using fractional Barbalat's lemma and constructing the Lyapunov function.Finally,the correctness of the theoretical results is verified by numerical simulations of different fractional-order values,and we found that the numerical solution of the fractional-order model has greater degrees of freedom.The increase of saturation constant in this model reflects the enhancement of protective measures for susceptible individuals,which can effectively ease the spread of disease.

关 键 词：SIVS传染病模型 分数阶 饱和发生率 Barbalat引理 全局渐近稳定性 

分 类 号：O175[理学—数学] R181[理学—基础数学]