期刊
JOURNAL OF DIFFERENTIAL EQUATIONS
卷 263, 期 12, 页码 8873-8915出版社
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jde.2017.08.066
关键词
Stochastic SIRS epidemic model; Piecewise deterministic Markov process; Stationary distribution; Omega-limit set; Attractor; Markov switching
类别
资金
- National Natural Science Foundation of China [11471089, 11771374, 11371048]
This paper studies the spread dynamics of a stochastic SIRS epidemic model with nonlinear incidence and varying population size, which is formulated as a piecewise deterministic Markov process. A threshold dynamic determined by the basic reproduction number R-0 is established: the disease can be eradicated almost surely if R-0 < 1, while the disease persists almost surely if R-0 > 1. The existing method for analyzing ergodic behavior of population systems has been generalized. The modified method weakens the required conditions and has no limitations for both the number of environmental regimes and the dimension of the considered system. When 72,0 > 1, the existence of a stationary probability measure is obtained. Furthermore, with the modified method, the global attractivity of the Omega-limit set of the system and the convergence in total variation to the stationary measure are both demonstrated under a mild extra condition. (C) 2017 Elsevier Inc. All rights reserved.
作者
我是这篇论文的作者
点击您的名字以认领此论文并将其添加到您的个人资料中。
推荐
暂无数据