期刊
JOURNAL OF DIFFERENTIAL EQUATIONS
卷 259, 期 12, 页码 7463-7502出版社
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jde.2015.08.024
关键词
Epidemic model; Markov semigroups; Reproduction number; Stationary distribution
类别
资金
- National Science Foundation of China [61373005]
- Zhejiang Provincial Natural Science Foundation, China [LY12A01014]
- NSF-DMS [1313312]
- Simons Collaboration Grants for Mathematicians [208902]
- College of Letters and Sciences
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.
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