一类具有转移和治疗机制的随机结核病模型的平稳分布与灭绝

吉林大学学报(理学版) ›› 2019, Vol. 57 ›› Issue (2): 235-242.

一类具有转移和治疗机制的随机结核病模型的平稳分布与灭绝

徐江1, 曹忠威2, 祖力3

1. 长春工业大学经济管理学院, 长春 130012; 2. 吉林财经大学应用数学学院, 长春 130117;3. 海南师范大学数学与统计学院, 海口 571158

收稿日期:2018-07-20 出版日期:2019-03-26 发布日期:2019-03-26
通讯作者: 曹忠威 E-mail:caozw963@sina.com

Stationary Distribution and Extinction of a Stochastic Tuberculosis Model with Immigration and Treatment Mechanism#br#

XU Jiang¹, CAO Zhongwei², ZU Li³

1. School of Economics and Management, Changchun University of Technology, Changchun 130012, China;2. School of Applied Mathematics, Jilin University of Finance and Economics, Changchun 130117, China;3. College of Mathematics and Statistics, Hainan Normal University, Haikou 571158, China

Received:2018-07-20 Online:2019-03-26 Published:2019-03-26
Contact: CAO Zhongwei E-mail:caozw963@sina.com

摘要/Abstract

摘要： 考虑一类具有转移和治疗机制的肺结核传播模型在随机扰动下的动力学行为. 首先, 通过Lyapunov分析方法得到该模型正解的存在和唯一性；然后利用Has’minskii理论证明该模型存在唯一的平稳分布；最后通过随机分析方法得到该模型疾病消失的条件.

关键词: 随机结核病模型, 平稳分布, 转移和治疗, 遍历性, 灭绝性

Abstract: We considered a dynamic behavior of a class of tuberculosis transmission model with immigration and treatment mechanism under random perturbations. Firstly, the existence and uniqueness of a positive solution of the model were obtianed by Lyapunov analysis method. Secondly, it was proved that the model had unique stationary distribution by using Has’minskii theory. Finally, the conditions for extinction of the disease were obtained by stochastic analysis method.

Key words: stochastic tuberculosis model, stationary distribution, immigration and treatment, , ergodicity, extinction

中图分类号:

O211.63

徐江, 曹忠威, 祖力. 一类具有转移和治疗机制的随机结核病模型的平稳分布与灭绝[J]. 吉林大学学报(理学版), 2019, 57(2): 235-242.

XU Jiang, CAO Zhongwei, ZU Li. Stationary Distribution and Extinction of a Stochastic Tuberculosis Model with Immigration and Treatment Mechanism#br#[J]. Journal of Jilin University Science Edition, 2019, 57(2): 235-242.

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