Stochastic virus infection model with Ornstein–Uhlenbeck perturbation: Extinction and stationary distribution analysis

Author:

Cao Zhongwei1,Guo Chenguang2,Shi Zhenfeng3,Song Zhifei4,Zu Li5ORCID

Affiliation:

1. Center for Teaching Faculty Development Jilin University of Finance and Economics Changchun Jilin China

2. School of Statistics Jilin University of Finance and Economics Changchun Jilin China

3. School of Mathematics and Statistics Northeast Normal University Changchun Jilin China

4. Personnel Office Jilin University Of Finance And Economics Changchun Jilin China

5. College of Mathematics and Statistics Hainan Normal University Haikou Hainan China

Abstract

In this paper, we propose a stochastic virus infection model with nonlytic immune response, where the transmission rate is realistically modeled as being subject to continuous fluctuations, represented by the Ornstein–Uhlenbeck process. Firstly, we establish the existence and uniqueness of the global solution for the stochastic model and its invariant set, ensuring the robustness and applicability of model. Next, by constructing appropriate Lyapunov functions, we derive sufficient conditions for virus extinction and the existence of a stationary distribution for the stochastic model. These conditions elucidate the key dynamic behaviors, such as extinction and persistence, within the stochastic framework.

Funder

National Natural Science Foundation of China

Publisher

Wiley

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