Threshold Dynamics of the Stochastic SIRC Epidemic Model - Journal of Applied Mathematics and Physics

JAMP > Vol.6 No.12, December 2018

Threshold Dynamics of the Stochastic SIRC Epidemic Model ()

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Download as PDF (Size: 1192KB) PP. 2498-2517

DOI: 10.4236/jamp.2018.612210 877 Downloads 1,882 Views Citations

Author(s)

Guangyang Zhang

Affiliation(s)

College of Science, University of Shanghai for Science and Technology, Shanghai, China.

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.

KEYWORDS

Stochastic SIRC Model, Stability, Threshold, Persistence in Mean, The Endemic Equilibrium

Share and Cite:

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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