## Abstract and Applied Analysis

### Global Stability of Multigroup SIRS Epidemic Model with Varying Population Sizes and Stochastic Perturbation around Equilibrium

Xiaoming Fan

#### Abstract

We discuss multigroup SIRS (susceptible, infectious, and recovered) epidemic models with random perturbations. We carry out a detailed analysis on the asymptotic behavior of the stochastic model; when reproduction number ${\scr R}_{0}>1$, we deduce the globally asymptotic stability of the endemic equilibrium by measuring the difference between the solution and the endemic equilibrium of the deterministic model in time average. Numerical methods are employed to illustrate the dynamic behavior of the model and simulate the system of equations developed. The effect of the rate of immunity loss on susceptible and recovered individuals is also analyzed in the deterministic model.

#### Article information

Source
Abstr. Appl. Anal., Volume 2014, Special Issue (2013), Article ID 154725, 14 pages.

Dates
First available in Project Euclid: 2 October 2014

https://projecteuclid.org/euclid.aaa/1412277375

Digital Object Identifier
doi:10.1155/2014/154725

Mathematical Reviews number (MathSciNet)
MR3166570

Zentralblatt MATH identifier
07021823

#### Citation

Fan, Xiaoming. Global Stability of Multigroup SIRS Epidemic Model with Varying Population Sizes and Stochastic Perturbation around Equilibrium. Abstr. Appl. Anal. 2014, Special Issue (2013), Article ID 154725, 14 pages. doi:10.1155/2014/154725. https://projecteuclid.org/euclid.aaa/1412277375

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