Asymptotic behavior of the solutions for a stochastic SIRS model with information intervention

Abstract

<abstract><p>In this paper, a stochastic SIRS epidemic model with information intervention is considered. By constructing an appropriate Lyapunov function, the asymptotic behavior of the solutions for the proposed model around the equilibria of the deterministic model is investigated. We show the average in time of the second moment of the solutions of the stochastic system is bounded for a relatively small noise. Furthermore, we find that information interaction response rate plays an active role in disease control, and as the intensity of the response increases, the number of infected population decreases, which is beneficial for disease control.</p></abstract>

Dynamics and stationary distribution of a stochastic SIRS epidemic model with a general incidence and immunity

“…Thus, the stochastic epidemic model can provide more realism than the corresponding deterministic models. In the past few years, many researchers have considered stochastic epidemic models and have obtained significant results [27,30,[32][33][34][35][36][37][38][39][40][41][42]. For example, Jiang et al [42] proved a global positive solution of a stochastic SIR model and investigated the asymptotic behaviors.…”

“…Koufi et al [34] considered a stochastic SIRS system with switching among different environments. Ding and Zhang [35] proposed a stochastic SIRS epidemic model with bilinear incidence. However, to the best of our knowledge, there are few reports of research about the stochastic SIRS model with general incidence and partial immunity.…”