Analysis of SIR epidemic model with relapse incorporating Ornstein-Uhlenbeck process

Abstract

In this work, we analyze a stochastic SIR epidemic model that incorporates the Ornstein--Uhlenbeck process, relapse, and generalized nonlinear incidence rate. First, we demonstrate that, under all favorable initial conditions, there is only one possible global solution. The new stochastic model threshold values, D_β and D_α, are created. We create the necessary conditions for the disease to persist and become extinct. Lastly, we present a few computer simulations that demonstrate the theoretical understanding we have acquired. Our findings highlight the importance of recognizing how stochasticity affects epidemic transmission, especially when complicated incidence mechanisms and stochastic environmental variables are involved.