Dynamic Analysis of a Stochastic Water-borne Epidemic Model

LIAO Shu, ZHANG Yu YANG, Weiming

Acta Mathematicae Applicatae Sinica ›› 2025, Vol. 48 ›› Issue (2) : 208-229.

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Acta Mathematicae Applicatae Sinica ›› 2025, Vol. 48 ›› Issue (2) : 208-229. DOI: 10.20142/j.cnki.amas.202401089

Dynamic Analysis of a Stochastic Water-borne Epidemic Model

  • LIAO Shu1, ZHANG Yu YANG2, Weiming2
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Abstract

In this paper, we study a water-borne epidemic model with multiple transmission ways. Firstly, we show the existence and uniqueness of global positive solution of the stochastic model by using suitable Lyapunov function. Moreover, by applying the Has'minskii theory, we obtain the existence of a ergodic stationary distribution of the positive solution of the model system under certain sufficient conditions. At last, we carry out numerical simulations to verify the analytical results. The results show that Random noise has a great influence on the spread of infectious diseases, and larger noise is beneficial to control the outbreak and spread of infectious diseases.

Key words

stochastic epidemic model / cholera / extinction / stationary distribution

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LIAO Shu , ZHANG Yu YANG , Weiming. Dynamic Analysis of a Stochastic Water-borne Epidemic Model. Acta Mathematicae Applicatae Sinica, 2025, 48(2): 208-229 https://doi.org/10.20142/j.cnki.amas.202401089

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