[1]蒋贵荣,杨 鲲,林 娇.一类具有非线性传染率和生育脉冲的随机SIS传染病模型的动力学分析[J].南京师范大学学报(自然科学版),2016,39(03):10.[doi:10.3969/j.issn.1001-4616.2016.03.002]
 Jiang Guirong,Yang Kun,Lin Jiao.Dynamics Analysis of a Stochastic SIS Epidemic Modelwith Nonlinear Incidence and Birth Pulses[J].Journal of Nanjing Normal University(Natural Science Edition),2016,39(03):10.[doi:10.3969/j.issn.1001-4616.2016.03.002]
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一类具有非线性传染率和生育脉冲的随机SIS传染病模型的动力学分析()
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《南京师范大学学报》(自然科学版)[ISSN:1001-4616/CN:32-1239/N]

卷:
第39卷
期数:
2016年03期
页码:
10
栏目:
·特约稿·
出版日期:
2016-09-30

文章信息/Info

Title:
Dynamics Analysis of a Stochastic SIS Epidemic Modelwith Nonlinear Incidence and Birth Pulses
文章编号:
1001-4616(2016)03-0010-06
作者:
蒋贵荣1杨 鲲2林 娇3
(1.桂林航天工业学院电子信息与自动化学院,广西 桂林 541004)(2.三门峡市外国语高级中学,河南 三门峡 472000)(3.百色学院数学与统计学院,广西 百色 533000)
Author(s):
Jiang Guirong1Yang Kun2Lin Jiao3
(1.College of Electronic Information and Automation,Guilin University of Aerospace Technology,Guilin 541004,China)(2.Sanmenxia Foreign Language High School,Sanmenxia,472000,China)(3.School of Mathematics and Statics,Baise University,Baise 533000,China)
关键词:
随机SIS传染病模型非线性传染率生育脉冲Lyapunov函数
Keywords:
stochastic SIS epidemic modelnonlinear incidencebirth pulsesLyapunov function
分类号:
O175.1
DOI:
10.3969/j.issn.1001-4616.2016.03.002
文献标志码:
A
摘要:
研究了一类具有非线性传染率、生育脉冲和随机干扰的SIS传染病模型. 通过建立Lyapunov函数证明了全局正解的存在唯一性,研究疾病是否消亡,得到了疾病灭绝的充分条件,利用随机非线性理论中Lyapunov指数,得到无病解随机指数渐近稳定的充分条件.
Abstract:
A stochastic SIS epidemic model with nonlinear incidence and birth pulses is investigated in this paper. The existence and uniqueness of the global positive solution are proved by establishing Lyapunov function. The sufficient condition for stochastic extinction of the infection is gained. The sufficient condition for the stochastically exponentially asymptotically stability of infection-free solution is gained by using the Lyapunov exponents.

参考文献/References:

[1] MAO X. Stochastic differential equation:theory and applications[M]. New York:Wiley,1972.
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[7] 周艳丽,张卫国. 非线性传染率的随机SIS传染病模型的持久性和灭绝性[J]. 山东大学学报(理学报),2013,48(10):68-77.
[8] 王伟华. 具有状态转换和时滞的随机生态模型的研究[D]. 南昌:南昌大学,2013:1-38.
[9] LIU J. Analysis of an epidemic model with density-dependent birth rate,birth pulses[J]. Communication in nonlinear science and numerical simulation,2010,15(1):3 568-3 576.
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备注/Memo

备注/Memo:
收稿日期:2015-11-13. 
基金项目:国家自然科学基金(11662001,11562006)、广西自然科学基金(2012GXNSFAA053006)、广西教育厅科研项目(KY2015YB112)、广西研究生教育创新计划项目(YCSZ2014143). 
通讯联系人:蒋贵荣,博士,教授,研究方向:非光滑动力系统动力学分析. E-mail:grjiang9@163.com
更新日期/Last Update: 2016-09-30