Open Access
2014 Dynamics of a Stochastic SIS Epidemic Model with Saturated Incidence
Can Chen, Yanmei Kang
Abstr. Appl. Anal. 2014: 1-13 (2014). DOI: 10.1155/2014/723825


We introduce stochasticity into the SIS model with saturated incidence. The existence and uniqueness of the positive solution are proved by employing the Lyapunov analysis method. Then, we carry out a detailed analysis on both its almost sure exponential stability and its pth moment exponential stability, which indicates that the pth moment exponential stability implies the almost sure exponential stability. Additionally, the results show that the conditions for the disease to become extinct are much weaker than those in the corresponding deterministic model. The conditions for the persistence in the mean and the existence of a stationary distribution are also established. Finally, we derive the expressions for the mean and variance of the stationary distribution. Compared with the corresponding deterministic model, the threshold value for the disease to die out is affected by the half saturation constant. That is, increasing the saturation effect can reduce the disease transmission. Computer simulations are presented to illustrate our theoretical results.


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Can Chen. Yanmei Kang. "Dynamics of a Stochastic SIS Epidemic Model with Saturated Incidence." Abstr. Appl. Anal. 2014 1 - 13, 2014.


Published: 2014
First available in Project Euclid: 2 October 2014

zbMATH: 07022951
MathSciNet: MR3226225
Digital Object Identifier: 10.1155/2014/723825

Rights: Copyright © 2014 Hindawi

Vol.2014 • 2014
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