1. Stationary distribution and density function analysis of a stochastic epidemic HBV model
- Author
-
Junyan Ge, Daqing Jiang, and Wenjie Zuo
- Subjects
Lyapunov function ,Numerical Analysis ,Stationary distribution ,General Computer Science ,Stochastic modelling ,Applied Mathematics ,Ergodicity ,Ode ,Probability density function ,Critical value ,Theoretical Computer Science ,symbols.namesake ,Modeling and Simulation ,symbols ,Quantitative Biology::Populations and Evolution ,Applied mathematics ,Basic reproduction number ,Mathematics - Abstract
In this paper, we present a stochastic hepatitis B virus (HBV) infection model and the dynamic behaviors of the model are investigated. When the fraction of vertical transmission μ ω ν C is not considered to be new infections, the existence and ergodicity of the stationary distribution of the model are obtained by constructing a suitable Lyapunov function, which determines a critical value ρ 0 s corresponding to the basic reproduction number of ODE system. This implies the persistence of the diseases when ρ 0 s > 1 . Meanwhile, the sufficient conditions for the extinction of the diseases are derived when ρ 0 T 0 . What is more, we give the specific expression of the probability density function of the stochastic model around the unique endemic quasi-equilibrium by solving the Fokker–Planck equation. Finally, the numerical simulations are illustrated to verify the theoretical results and match the HBV epidemic data in China.
- Published
- 2022