一类具有传播媒介的SIS传染病模型的动力学性态分析
Dynamic Behavior Analysis of a Class of SIS Infectious Disease Models with Vectors
摘要: 随着传媒技术的进步和成熟，媒体对疾病疫情的报道产生的影响已经成为人们预防和控制疾病传播不可忽略的因素之一。文中考虑了疾病信息意识影响，建立了一个新的具有媒介影响的SIS传染病模型。首先，对建立的具有媒介影响的新的SIS传染病模型讨论了无病平衡点和地方病平衡点的存在性和基本再生数。其次，应用Routh-Hurwitz判别准则分别证明了无病平衡点和地方病平衡点的局部渐近稳定性的满足条件。紧接着构造了恰当Lyapunov函数并结合LaSalle不变原理，分别讨论了无病平衡点和地方病平衡点在不同阈值条件下的全局渐近稳定性。最后进行了数值模拟，验证在不同阈值条件下系统的稳定性，比较参数在不同取值时平衡点的变化，分析传染病的发展规律。数值模拟的结果与理论分析的结果是吻合的。
Abstract: With the progress and maturity of media technology, the influence of media on the report of disease has become one of the factors that can not be ignored for people to prevent and control the spread of disease. In this paper, a new SIS infectious disease model with vector influence is established by considering the influence of disease information awareness. First, the existence and basic regeneration numbers of disease-free equilibrium and endemic equilibrium points are discussed for a new model of SIS infectious disease with vector influence. Secondly, the routh-Hurwitz criterion is applied to prove the local asymptotic stability of disease-free equilibrium and endemic equilibrium. Then an appropriate Lyapunov function is constructed and LaSalle invariance princi-ple is used to discuss the global asymptotic stability of disease-free equilibrium and endemic equi-librium under different threshold conditions. Finally, numerical simulation is carried out to verify the stability of the system under different threshold conditions, compare the changes of equilibri-um point when the parameters are different values, and analyze the development law of infectious diseases. The results of numerical simulation agree well with those of theoretical analysis.
文章引用：代林烽, 陈龙伟. 一类具有传播媒介的SIS传染病模型的动力学性态分析[J]. 理论数学, 2023, 13(2): 294-306. https://doi.org/10.12677/PM.2023.132033

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