具有Markov切换的随机多群体SIRI动力学行为
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国家自然科学基金面上项目(No.11971081);重庆市教育委员会科技研究重大项目(No.KJZD-M202000502);重庆市研究生科研创新项目(No.CYS20242)


Dynamical Behavior of a Multigroup SIRI Epidemic Model with Markovian Switching
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    【目的】研究一类具有Markov切换的随机多群体SIRI模型。【方法】首先利用随机微分方程的基本理论给出模型解是正的、存在的、唯一的。再通过构造一些适当的新的Lyapunov函数,利用图论知识和不等式放缩技巧,获得了该传染病模型灭绝和持久的充分条件。【结果】得到该随机系统正解的存在唯一性,同时获得了疾病灭绝和在均值意义下持久的充分条件,得到了没有随机干扰时模型的阈值。【结论】通过分析可知调节系统的参数,即可以采取某些策略来调节疾病的动态,抑制疾病的爆发。

    Abstract:

    [Purposes]A stochastic multigroup SIRI model with markovian switching is studied. [Methods]Firstly, by using the basic theory of stochastic differential equations, the model solution is obtained to be positive, existing and unique. Secondly, by constructing some appropriate new Lyapunov functions and applying the knowledge of graph theory and the inequality scaling skills, the sufficient conditions for the extinction and persistence of the epidemic model are obtained. [Results]The existence and uniqueness of the positive solution of the stochastic system are obtained. At the same time, the sufficient conditions for disease extinction and persistence in the mean of the disease are obtained. The threshold for the model without random disturbance is obtained. [Conclusions]By analyzing theorem 1, the parameters of the adjustment system can be adjusted, that is, some strategies can be adopted to adjust the dynamics of the disease and suppress the outbreak of the disease.

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邓涵,张志成,杨志春.具有Markov切换的随机多群体SIRI动力学行为[J].重庆师范大学学报自然科学版,2023,40(3):86-93

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  • 在线发布日期: 2023-07-27