JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2026, Vol. 61 ›› Issue (7): 1-17.doi: 10.6040/j.issn.1671-9352.0.2024.422

• Mathematical Biology •    

Dynamic analysis of a cholera epidemic model with Markov switching

LIAO Shu1, XIA Nannan1, DUAN Wenlong2   

  1. 1. School of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067, China;
    2. School of Software, Chongqing Finance and Economics College, Chongqing 401320, China
  • Published:2026-07-01

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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 Re for the extinction of the disease and Rc for the stationary distribution are obtained. When Rc>1, the model has a unique ergodic stationary distribution;when Re<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

CLC Number: 

  • O175
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