Mathematical modeling reveals that increased media coverage reduces infection levels in a stochastic SIRI framework, indicating that public awareness promotes epidemic extinction.
In this paper, we mainly consider the dynamics of a stochastic SIRI epidemic model with media coverage. Firstly, a sufficient condition for the existence and uniqueness of the ergodic stationary distribution of the model is obtained by establishing an appropriate Lyapunov function. Then the approximate expression of probability density function of the solution to this model around quasi-endemic equilibrium is obtained by solving the corresponding Fokker-Planck equation. In addition, the sufficient conditions for the extinction of the disease are given. Finally, some numerical simulations are introduced to verify our theoretical results. The results indicate that as media coverage parameter increases, the time average of infected individuals decreases, which implies that media coverage can promote the extinction of disease.
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Liu et al. (2026) studied this question.
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