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转换机制下具有非线性发生率的随机SIRS传染病模型的动力学性质

发表时间:2018-01-15  浏览量:753  下载量:23
全部作者: 胡俊娜,李智明,滕志东
作者单位: 新疆大学数学与系统科学学院
摘 要: 研究一类转换机制下具有非线性发生率的随机SIRS传染病模型的动力学性质。首先给出随机传染病模型的一些结论和连续时间的马尔可夫过程的定义,利用M-矩阵方法证明当疾病灭绝时传染病模型唯一正解的存在性,并对模型的唯一遍历稳态分布解的存在性的充分条件进行分析和研究;然后给出一个新的基本再生数 的定义,并通过建立适当的Lyapunov函数和Itô’s公式,确立了疾病灭绝和持久性的判别条件,即当R_{0}^{S}<0时,疾病是依概率1灭绝的;当R_{0}^{S}>0时,疾病是依概率1持久的。
关 键 词: 应用数学;随机SIRS传染病模型;灭绝性;持久性;阈值;非线性发生率
Title: Dynamics behavior of a stochastic SIRS epidemic model with nonlinear incidence rate under regime switching
Author: HU Junna, LI Zhiming, TENG Zhidong
Organization: College of Mathematics and System Science, Xinjiang University
Abstract: In this paper, the dynamics behavior of a stochastic SIRS epidemic model with nonlinear incidence rate under regime switching is investigated. Firstly, some conclusions of stochastic epidemic model and definition of Markov process for continuous time are given. The M-matrix method is used to prove the existence of a unique positive solution to the epidemic model when the disease is extinct. The sufficient conditions established for the existence of a unique ergodic stationary distribution solution of the model are also analyzed and studied. Then a new definition of basic reproductive number is given and the conditions of extinction and persistence of disease are built up by establishing the appropriate Lyapunov function and the Itô’s formula. The disease dies out with probability one when R_{0}^{S}<0, while the disease is permanent with probability one when R_{0}^{S}>0.
Key words: applied mathematics; stochastic SIRS epidemic model; extinction; permanence; threshold; nonlinear incidence rate
发表期数: 2018年1月第1期
引用格式: 胡俊娜,李智明,滕志东. 转换机制下具有非线性发生率的随机SIRS传染病模型的动力学性质[J]. 中国科技论文在线精品论文,2018,11(1):17-27.
 
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