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Analysis of a stochastic SEI I R epidemic model incorporating the Ornstein-Uhlenbeck process
Mhammed Mediani1, Abdeldjalil Slama1, Ahmed Boudaoui1
1Laboratory of Mathematics, Modeling and Applications (LaMMA), University of Adrar, Adrar, Algeria.
Abstract:
This article aims to analyze a stochastic epidemic model (Susceptible-exposed-undetected infected-detected infected (reported -recovered) assuming that the transmission rate at which people undetected become detected is perturbed by the Ornstein-Uhlenbeck process. Our first objective is to prove that the stochastic model has a unique positive global solution by constructing a nonnegative Lyapunov function. Afterward, we provide a sufficient criterion to prove the existence of an ergodic stationary distribution of the mode by constructing a suitable series of Lyapunov functions. Subsequently, we establish sufficient conditions for the extinction of the disease. Finally, a series of numerical simulations are carried out to illustrate the theoretical results.
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