A stochastic examination of the SIRI epidemic model including nonlinear relapse and the Ornstein-Uhlenbeck process

Abstract

In this study, we conduct an analysis of a stochastic SIRI model with nonlinear relapse that incorporates the Ornstein–Uhlenbeck process. Initially, we establish the existence of a unique global positive solution. Then, we present the sufficient conditions for both disease extinction and persistence. By constructing an appropriate Lyapunov function, we further demonstrate the existence of a stationary distribution for our model. Finally, we present some computer simulations that demonstrate the theoretical insights that we have obtained. The results of this study have the potential to enhance our understanding of epidemic models and contribute to the development of viable strategies for disease prevention and control.