Document Type
Article
Publication Date
Spring 2-1-2026
Abstract
In this study, we develop and investigate a stochastic $SEI_{u}I_{r}RS$ (Susceptible-Exposed-Undetected infected-Detected infected-Recovered-Susceptible) epidemic model with vaccination of newborns and the disease transmission rate driven by a log-normal Ornstein-Uhlenbeck process. By establishing a series of Lyapunov functions, we derive sufficient conditions for persistence in the mean of the disease in the long term under the condition $\mathcal{R}_{0}>1$ and these criteria are applied to guarantee the existence of an invariant probability measure of the stochastic system. Subsequently, we also derive sufficient conditions for eradication of the disease when the parameters $\mathcal{R}_{0}< 1$ and $\mathcal{R}_{0}^{E}< 1$. Finally, two numerical examples are given to confirm the theoretical results. This work can help us implement interventions to regulate the disease dynamics.
Publication Source (Journal or Book title)
Journal
Recommended Citation
Liu, Q. (2026). Dynamical analysis of a stochastic $SEI_{u}I_{r}RS$ epidemic model with vaccination and log-normal Ornstein-Uhlenbeck process. Journal Retrieved from https://repository.lsu.edu/mathematics_pubs/1430
Comments
In previous references, few researchers have focused on analyzing the global dynamics of a stochastic $SEI_{u}I_{r}RS$ epidemic model with vaccination of newborns and log-normal Ornstein-Uhlenbeck process. This stochastic framework contributes greatly to the field by studying the dynamical properties of the stochastic system (1.2) while guaranteeing ecological rationality. The model presented here serves as a foundation for further study, including the investigation of long time behavior, global asymptotical stability, and the effects of random perturbations on disease dynamics.