Stationary distribution of a stochastic HLIV epidemic model with viral production and mean-reverting inhomogeneous geometric Brownian motion

Abstract

In this work, we investigate a stochastic HLIV model incorporating viral dynamics, in which the mean-reverting inhomogeneous geometric Brownian motion process (IGBM for short) perturb the conversion rate from eclipse phase cells to infected cells. We first establish the existence and uniqueness of a positive solution and show that the model admits a unique global solution for any given initial condition. We then employ stochastic Lyapunov functions together with Fatou's lemma to derive sufficient conditions for the existence of a stationary distribution of positive solution, thereby indicating strong persistence of the disease. Finally, we conclude by summarizing the main results and implications of our study.