The Influence of Environmental Variability and Media Coverage on the Dynamics of an Epidemic Model (Journal of Nonlinear Modeling and Analysis, 2025)
Various infectious diseases seriously affect human health and socialeconomy. It is a never-ending battle that human beings fight against infectious diseases. Media coverage has been an important weapon in virus war andhas contributed to the epidemic prevention. In this paper, we focus on thedynamics of a stochastic SIRS epidemic model with media coverage and twomean-reverting Ornstein-Uhlenbeck processes. Firstly, we present the existence and uniqueness of the solution. Then, the sufficient condition for diseaseextinction is provided. In order to get the condition for disease persistence,we verify the existence of stationary distribution by constructing appropriateLyapunov functions. Moreover, it is theoretically proved that the solution follows a normal probability density function around the endemic equilibrium ofcorresponding deterministic model. Finally, some numerical simulations arecarried out to confirm theoretical results.