1. The asymptotic behavior and ergodicity of stochastically perturbed SVIR epidemic model.
- Author
-
Zhao, Yanan and Jiang, Daqing
- Subjects
- *
VACCINATION , *COMMUNICABLE diseases , *LYAPUNOV functions , *STOCHASTIC differential equations , *BROWNIAN motion - Abstract
In this paper, we introduce stochasticity into an SIR epidemic model with vaccination. The stochasticity in the model is a standard technique in stochastic population modeling. When the perturbations are small, by the method of stochastic Lyapunov functions, we carry out a detailed analysis on the dynamical behavior of the stochastic model regarding of the basic reproduction number . If , the solution of the model is oscillating around a steady state, which is the disease-free equilibrium of the corresponding deterministic model. If , there is a stationary distribution and the solution has the ergodic property, which means that the disease will prevail. [ABSTRACT FROM AUTHOR]
- Published
- 2016
- Full Text
- View/download PDF