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- Title
Dynamical behaviors of a stochastic SIRV epidemic model with the Ornstein–Uhlenbeck process.
- Authors
Shang, Jiaxin; Li, Wenhe
- Abstract
Vaccination is an important tool in disease control to suppress disease, and vaccine-influenced diseases no longer conform to the general pattern of transmission. In this paper, by assuming that the infection rate is affected by the Ornstein–Uhlenbeck process, we obtained a stochastic SIRV model. First, we prove the existence and uniqueness of the global positive solution. Sufficient conditions for the extinction and persistence of the disease are then obtained. Next, by creating an appropriate Lyapunov function, the existence of the stationary distribution for the model is proved. Further, the explicit expression for the probability density function of the model around the quasi-equilibrium point is obtained. Finally, the analytical outcomes are examined by numerical simulations.
- Subjects
ORNSTEIN-Uhlenbeck process; PROBABILITY density function; EPIDEMICS; LOTKA-Volterra equations; LYAPUNOV functions; PREVENTIVE medicine
- Publication
Advances in Continuous & Discrete Models, 2024, Vol 2024, Issue 1, p1
- ISSN
2731-4235
- Publication type
Article
- DOI
10.1186/s13662-024-03807-6