A generalized stochastic SIRS epidemic model incorporating mean-reverting Ornstein-Uhlenbeck process

The aim of this work is to study a new stochastic SIRS epidemic model that includes the mean-reverting Ornstein-Uhlenbeck process and a general incidence rate. First, we prove the global existence and positivity of the solution by using Lyapunov functions. Second, we analytically make out the stochastic epidemic threshold (T) over tilde (S)(0) which pilots the extinction and persistence in mean of the disease. We have proven that the disease extinguishes when (T) over tilde (S)(0) < 1. Otherwise, if <(T)over tilde>(S)(0) > 1, then disease is persistent in mean. For the critical case (T) over tilde (S)(0) = 1, we have shown that the disease dies out by using an approach involving some appropriate stopping times. Finally, we present a series of numerical simulations to confirm the feasibility and correctness of the theoretical analysis results. (c) 2023 Elsevier B.V. All rights reserved.

Automated summary

The aim of this study is to analyze a new stochastic SIRS epidemic model incorporating the mean-reverting Ornstein-Uhlenbeck process and a general incidence rate. The global existence and positivity of the solution are proven using Lyapunov functions. The stochastic epidemic threshold (T) over tilde (S)(0), which determines disease extinction or persistence, is analytically determined. Numerical simulations are conducted to validate the theoretical results.