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Threshold Dynamics of the Stochastic SIRC Epidemic Model

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Document pages: 20 pages

Abstract: In this paper, we discuss thedynamics of a stochastic SIRC epidemic model with infection rate affected bywhite noise. We prove that this stochastic model has a unique nonnegativesolution globally. A threshold is identified. When the noise is small, the solution of the stochastic model converges to thedisease-free equilibrium point of the deterministic model if , which means the basicreproductive number of the stochastic model. And if , the solution of thestochastic model fluctuates around the epidemic equilibrium of thedeterministic model. When the noise is large, the disease tends to extinction.The results are illustrated by computer simulations.

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