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<p>Considering the diversity of disease transmission pathways, delay effects, and the significant impacts of random factors on disease spread, we propose a stochastic Susceptible-Infected-Recovered-Environment (SIRW) epidemic model with infinite distributed delay. In this model, the recovery rate of the infected class and the virus emission rate follow the Black-Karasinski process. First, the existence and uniqueness of the global positive solution for the model are proved. Next, by combining spectral radius theory, a sufficient condition for extinction is derived, implying the elimination of both the disease and environmental viruses. Then, using Markov process stability theory and stochastic Lyapunov function techniques, we establish the criteria for the existence of a stationary distribution, which indicates the persistence of the disease and environmental viruses. In particular, by applying the theory of algebraic equations, the unique expression for the probability density function around the quasi-endemic equilibrium is deduced. This characterizes the statistical features of individuals across different compartments. Finally, numerical examples illustrate the accuracy of the theoretical results and reveal the effects of perturbation intensities and key parameters on disease transmission. Based on these findings, we develop a targeted strategy to control disease spread, supporting public health policies.</p>

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Dynamical analysis of a stochastic SIRW model with distributed delay and Black-Karasinski process

  • 期刊论文

  • 发表日期：

    2025年5月13日

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  • Hong Cao,
  • Xiaohu Liu,
  • Jingyun Shen,
  • Linfei Nie

摘要

Considering the diversity of disease transmission pathways, delay effects, and the significant impacts of random factors on disease spread, we propose a stochastic Susceptible-Infected-Recovered-Environment (SIRW) epidemic model with infinite distributed delay. In this model, the recovery rate of the infected class and the virus emission rate follow the Black-Karasinski process. First, the existence and uniqueness of the global positive solution for the model are proved. Next, by combining spectral radius theory, a sufficient condition for extinction is derived, implying the elimination of both the disease and environmental viruses. Then, using Markov process stability theory and stochastic Lyapunov function techniques, we establish the criteria for the existence of a stationary distribution, which indicates the persistence of the disease and environmental viruses. In particular, by applying the theory of algebraic equations, the unique expression for the probability density function around the quasi-endemic equilibrium is deduced. This characterizes the statistical features of individuals across different compartments. Finally, numerical examples illustrate the accuracy of the theoretical results and reveal the effects of perturbation intensities and key parameters on disease transmission. Based on these findings, we develop a targeted strategy to control disease spread, supporting public health policies.