J. Nonl. Mod. Anal., 7 (2025), pp. 514-551.
Published online: 2025-04
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Various infectious diseases seriously affect human health and social economy. It is a never-ending battle that human beings fight against infectious diseases. Media coverage has been an important weapon in virus war and has contributed to the epidemic prevention. In this paper, we focus on the dynamics of a stochastic SIRS epidemic model with media coverage and two mean-reverting Ornstein-Uhlenbeck processes. Firstly, we present the existence and uniqueness of the solution. Then, the sufficient condition for disease extinction is provided. In order to get the condition for disease persistence, we verify the existence of stationary distribution by constructing appropriate Lyapunov functions. Moreover, it is theoretically proved that the solution follows a normal probability density function around the endemic equilibrium of corresponding deterministic model. Finally, some numerical simulations are carried out to confirm theoretical results.
}, issn = {2562-2862}, doi = {https://doi.org/10.12150/jnma.2025.514}, url = {http://global-sci.org/intro/article_detail/jnma/24014.html} }Various infectious diseases seriously affect human health and social economy. It is a never-ending battle that human beings fight against infectious diseases. Media coverage has been an important weapon in virus war and has contributed to the epidemic prevention. In this paper, we focus on the dynamics of a stochastic SIRS epidemic model with media coverage and two mean-reverting Ornstein-Uhlenbeck processes. Firstly, we present the existence and uniqueness of the solution. Then, the sufficient condition for disease extinction is provided. In order to get the condition for disease persistence, we verify the existence of stationary distribution by constructing appropriate Lyapunov functions. Moreover, it is theoretically proved that the solution follows a normal probability density function around the endemic equilibrium of corresponding deterministic model. Finally, some numerical simulations are carried out to confirm theoretical results.