TITLE:
Threshold Dynamics of the Stochastic SIRC Epidemic Model
AUTHORS:
Guangyang Zhang
KEYWORDS:
Stochastic SIRC Model, Stability, Threshold, Persistence in Mean, The Endemic Equilibrium
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.6 No.12,
December
11,
2018
ABSTRACT: In this paper, we discuss the
dynamics of a stochastic SIRC epidemic model with infection rate affected by
white noise. We prove that this stochastic model has a unique nonnegative
solution globally. A threshold is identified. When the noise is small, the solution of the stochastic model converges to the
disease-free equilibrium point of the deterministic model if , which means the basic
reproductive number of the stochastic model. And if , the solution of the
stochastic model fluctuates around the epidemic equilibrium of the
deterministic model. When the noise is large, the disease tends to extinction.
The results are illustrated by computer simulations.