一类具有两菌株突变的传染病模型
A Class of Infectious Disease Models with Mutations in Two Strains
摘要: 病原体在传播过程中所引起的变异严重影响对于疾病传播动力学的分析。为了更好地了解病原体突变对疾病传播的影响，本文建立了一个具有两菌株在传播过程中发生变异的传染病模型。我们主要用常微分方程描述了宿主内两种菌株变异的传染病模型，采用在模型平衡点处线性化的方法，分析了该模型的平衡点以及平衡点附近的稳定性。我们得出在模型在无病平衡点处是全局渐近稳定的，模型在边界平衡点处是局部渐近稳定的，最后我们给出了模型共存平衡点存在的条件。
Abstract: The variation caused by the pathogen during transmission has a serious impact on the analysis of disease transmission dynamics. In order to better understand the effects of pathogens mutation on the spread of disease, the article established a mutation in the process of two strains in the spread of infectious disease model. We describe an infectious disease model with variation of two strains in the host mainly by ordinary differential equations, and analyze the stability of the model at and near the equilibrium point by linearizing the equilibrium point of the model. We know that the model is globally asymptotically stable at the disease-free equilibrium point and locally asymp-totically stable at the boundary equilibrium point. Finally, we give the conditions for the existence of coexistence equilibrium.
文章引用：赵江月. 一类具有两菌株突变的传染病模型[J]. 理论数学, 2022, 12(10): 1585-1592. https://doi.org/10.12677/PM.2022.1210172

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