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 JAMP  Vol.6 No.12 , December 2018
Threshold Dynamics of the Stochastic SIRC Epidemic Model
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.
Cite this paper: Zhang, G. (2018) Threshold Dynamics of the Stochastic SIRC Epidemic Model. Journal of Applied Mathematics and Physics, 6, 2498-2517. doi: 10.4236/jamp.2018.612210.
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