A stochastic SIRS epidemic model with infectious force under intervention strategies

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:259

Article

Cai, Yongli¹  Kang, Yun²  Banerjee, Malay³  Wang, Weiming¹ 

[1] Huaiyin Normal Univ, Sch Math Sci, Huaian 223300, Peoples R China

[2] Arizona State Univ, Sci & Math Fac, Coll Letters & Sci, Mesa, AZ 85212 USA

[3] Indian Inst Technol, Dept Math & Stat, Kanpur 208016, Uttar Pradesh, India

关键词: Epidemic model;    Markov semigroups;    Reproduction number;    Stationary distribution;   

DOI  :  10.1016/j.jde.2015.08.024

来源: Elsevier

【 摘 要 】

In this paper, we extend a classical SIRS epidemic model with the infectious forces under intervention strategies from a deterministic framework to a stochastic differential equation (SDE) one through introducing random fluctuations. The value of our study lies in two aspects. Mathematically, by using the Markov semigroups theory, we prove that the reproduction number R-0(S) can be used to govern the stochastic dynamics of SDE model If R-0(S) < 1, under mild extra conditions, the SDE system has a disease-free absorbing set which means the extinction of disease with probability one. If R-0(S) > 1, under mild extra conditions, it has an endemic stationary distribution which leads to the stochastical persistence of the disease. Epidemiologically, we find that random fluctuations can suppress disease outbreak, which can provide us some useful control strategies to regulate disease dynamics. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free