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<p>In this paper, an epidemiologic model of SIRS with mean-reverting Ornstein-Uhlenbeck process is investigated, taking into account the vertical transmission of the epidemic. Firstly, the existence of a unique global positive solution to the stochastic SIRS model is proved. Secondly, we construct several appropriate Lyapunov functions to get the smooth distribution of the model and verify its ergodicity. Then, we also obtain sufficient conditions for disease persistence and extinction. Moreover, by solving the corresponding matrix equations, an exact expression for the probability density function in the vicinity of the local equilibrium can be obtained. Finally, the theoretical calculations were verified by numerical simulations.</p>

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Stationary distributions and density functions of a stochastic SIRS model with vertical transmission and ornstein-uhlenbeck process

  • 期刊论文

  • 发表日期：

    2025年6月28日

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  • Siyuan Jiao,
  • Jing Fu

摘要

In this paper, an epidemiologic model of SIRS with mean-reverting Ornstein-Uhlenbeck process is investigated, taking into account the vertical transmission of the epidemic. Firstly, the existence of a unique global positive solution to the stochastic SIRS model is proved. Secondly, we construct several appropriate Lyapunov functions to get the smooth distribution of the model and verify its ergodicity. Then, we also obtain sufficient conditions for disease persistence and extinction. Moreover, by solving the corresponding matrix equations, an exact expression for the probability density function in the vicinity of the local equilibrium can be obtained. Finally, the theoretical calculations were verified by numerical simulations.