Open Access
2013 Stochastic Dynamics of an SIRS Epidemic Model with Ratio-Dependent Incidence Rate
Yongli Cai, Xixi Wang, Weiming Wang, Min Zhao
Abstr. Appl. Anal. 2013(SI18): 1-11 (2013). DOI: 10.1155/2013/172631


We investigate the complex dynamics of an epidemic model with nonlinear incidence rate of saturated mass action which depends on the ratio of the number of infectious individuals to that of susceptible individuals. We first deal with the boundedness, dissipation, persistence, and the stability of the disease-free and endemic points of the deterministic model. And then we prove the existence and uniqueness of the global positive solutions, stochastic boundedness, and permanence for the stochastic epidemic model. Furthermore, we perform some numerical examples to validate the analytical findings. Needless to say, both deterministic and stochastic epidemic models have their important roles.


Download Citation

Yongli Cai. Xixi Wang. Weiming Wang. Min Zhao. "Stochastic Dynamics of an SIRS Epidemic Model with Ratio-Dependent Incidence Rate." Abstr. Appl. Anal. 2013 (SI18) 1 - 11, 2013.


Published: 2013
First available in Project Euclid: 26 February 2014

zbMATH: 1302.92123
MathSciNet: MR3064537
Digital Object Identifier: 10.1155/2013/172631

Rights: Copyright © 2013 Hindawi

Vol.2013 • No. SI18 • 2013
Back to Top