一类具有Markov切换的霍乱传染病模型的动力学分析

doi:10.6040/j.issn.1671-9352.0.2024.422

摘要/Abstract

摘要： 研究一个同时受白噪声影响和带有Markov切换的随机霍乱传染病模型,且带有一般性传染率函数和隔离措施。首先,得出模型的全局正解的存在唯一性。其次通过构造适当的随机Lyapunov函数,求出疾病是否灭绝的充分条件R_e和平稳分布的充分条件R_c。当R_c>1时,模型存在唯一遍历的平稳分布,当R_e<1时,疾病以指数速率灭绝。最后,通过数值模拟验证理论结果的正确性。结果表明较大强度的白噪声会导致传染病灭绝。若疾病在一个状态为持续,在另一个状态为灭绝,最终疾病灭绝还是持久取决于Markov链在每个状态下的概率大小。同时隔离措施也是疫情防控的重要措施之一。

关键词: 随机霍乱模型, Markov链, 灭绝性, 平稳分布

Abstract: A stochastic cholera epidemic model with Markov switching and affected by white noise is studied, with general transmission rates and isolation measures. Firstly, the existence and uniqueness of the global positive solution of the model are obtained. Secondly,by constructing appropriate stochastic Lyapunov functions,the sufficient conditions R_e for the extinction of the disease and R_c for the stationary distribution are obtained. When R_c>1, the model has a unique ergodic stationary distribution;when R_e<1, the disease dies out exponentially. Finally,numerical simulations are used to verify the above theoretical results. The results show that higher white noise intensity can lead to the extinction of infectious diseases. If the disease persists in one state and becomes extinct in another, whether the disease ultimately becomes extinct or persists depends on the probability distribution of the Markov chain across each state. Additionally,isolation measure is also an important method for epidemic prevention and control.

Key words: stochastic cholera model, Markov chain, extinction, stationary distribution

中图分类号:

O175

廖书,夏楠楠,段文龙. 一类具有Markov切换的霍乱传染病模型的动力学分析[J]. 《山东大学学报(理学版)》, 2026, 61(7): 1-17.

LIAO Shu, XIA Nannan, DUAN Wenlong. Dynamic analysis of a cholera epidemic model with Markov switching[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2026, 61(7): 1-17.

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