Analysis of the deterministic and stochastic SIRS epidemic models with nonlinear incidence

Qun Liu and Qingmei Chen

Physica A: Statistical Mechanics and its Applications, 2015, vol. 428, issue C, 140-153

Abstract: In this paper, the deterministic and stochastic SIRS epidemic models with nonlinear incidence are introduced and investigated. For deterministic system, the basic reproductive number R0 is obtained. Furthermore, if R0≤1, then the disease-free equilibrium is globally asymptotically stable and if R0>1, then there is a unique endemic equilibrium which is globally asymptotically stable. For stochastic system, to begin with, we verify that there is a unique global positive solution starting from the positive initial value. Then when R0>1, we prove that stochastic perturbations may lead the disease to extinction in scenarios where the deterministic system is persistent. When R0≤1, a result on fluctuation of the solution around the disease-free equilibrium of deterministic model is obtained under appropriate conditions. At last, if the intensity of the white noise is sufficiently small and R0>1, then there is a unique stationary distribution to stochastic system.

Keywords: Extinction; Stationary distribution; Nonlinear incidence; Itô’s formula; Lyapunov function (search for similar items in EconPapers)
Date: 2015
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (22)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378437115000941
Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:428:y:2015:i:c:p:140-153

DOI: 10.1016/j.physa.2015.01.075

Access Statistics for this article

Physica A: Statistical Mechanics and its Applications is currently edited by K. A. Dawson, J. O. Indekeu, H.E. Stanley and C. Tsallis

More articles in Physica A: Statistical Mechanics and its Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().