含有预防接种的霍乱时滞模型的稳定性和hopf分支分析

删除或更新信息，请邮件至freekaoyan#163.com(#换成@)

本站小编 Free考研考试/2021-12-27

含有预防接种的霍乱时滞模型的稳定性和hopf分支分析杨炜明, 廖书重庆工商大学数学与统计学院, 重庆 400067 Stability and Hopf-bifurcation of a Delay Cholera Model with Vaccination and Insecticides YANG Weiming, LIAO ShuSchool of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067, China

摘要
图/表
参考文献
相关文章(15)
点击分布统计
下载分布统计
-->

全文: PDF(660 KB) HTML (1 KB)
输出: BibTeX | EndNote (RIS)

摘要本文旨在建立一个包含预防接种并且具有复杂的传播途径的霍乱时滞模型.研究模型稳定性，以时滞为分支参数，通过分析相应特征方程根的分布，得出当时滞大小超过一个阙值时，系统稳定性发生变化，产生Hopf分支.其次利用中心流形定理和规范型理论研究分支方向，分支周期解稳定性和计算公式.最后以2008年津巴布韦霍乱为例进行模型数值模拟.

服务

加入引用管理器

E-mail Alert

RSS

收稿日期: 2016-07-08

PACS:

O29

基金资助:重庆市基础研究与前沿探索（cstc2017jcyjAX0067；cstc2018jcyjAX0823），重庆市教委科学技术研究（KJ1706163；KJ1600610）以及经济社会应用统计重庆市重点实验室资助项目.

引用本文:

杨炜明, 廖书. 含有预防接种的霍乱时滞模型的稳定性和hopf分支分析[J]. 应用数学学报, 2018, 41(6): 735-749. YANG Weiming, LIAO Shu. Stability and Hopf-bifurcation of a Delay Cholera Model with Vaccination and Insecticides. Acta Mathematicae Applicatae Sinica, 2018, 41(6): 735-749.

链接本文:

http://123.57.41.99/jweb_yysxxb/CN/或 http://123.57.41.99/jweb_yysxxb/CN/Y2018/V41/I6/735

[1]	Codeco C T. Endemic and epidemic dynamics of cholera:the role of the aquatic reservoir. BMC Infectious Diseases, 2001, 1:1
[2]	Hartley D M, Morris J G, Smith D L. Hyperinfectivity:a critical element in the ability of V. cholerae to cause epidemics? PLoS Medicine, 2006, 3(1):0063-0069
[3]	Liao S, Wang J. Stability Analysis and Application of a Mathematical Cholera Model. Mathematical Biosciences and Engineering, 2011, 8(3):733-752
[4]	Tien J H, Earn D J D. Multiple transmission pathways and disease dynamics in a waterborne pathogen model. Bulletin of mathematical biology, 2010, 72(6):1506-1533
[5]	Shuai Z, Driessche P V D. Global dynamics of cholera models with differential infectivity. Mathematical Biosciences, 2011, 234(2):118-126
[6]	Wang Y, Cao J. Global stability of general cholera models with nonlinear incidence and removal rates. Journal of the Franklin Institute, 2015, 352(6):2464-2485
[7]	Wang Y, Cao J. Global dynamics of a network epidemic model for waterborne diseases spread. Applied Mathematics and Computation, 2014, 237:474-488
[8]	Cao J, Wang Y, Alofi A, Elaiw A M. Global stability of an epidemic model with carrier state in heterogeneous networks. IMA Journal of Applied Mathematics, 2015, 80(4):1025-1048
[9]	Sanches R P, Ferreira C P, Kraenkel R A. The role of immunity and seasonality in cholera epidemic. Bulletin of Mathematical Biology, 2011, 73(12):2916-2931
[10]	Joh R I, Wang H, Weiss H, Weitz J S. Dynamics of indirectly transmitted infectious diseases with immunological threshold. Bulletin of Mathematical Biology, 2009, 71(4):845-862
[11]	Wang J, Chairat M. Modeling cholera dynamics with controls. Canadian applied mathematics quarterly, 2011, 19(3):255-273
[12]	Mukandavire Z, Liao S, Wang J, Gaff H, Smith D L, Morris J G. Estimating the reproductive numbers for the 2008-2009 cholera outbreaks in Zimbabwe. Proc. Natl Acad. Sci., 2011, 108(21):8767-8772
[13]	Liao S, Yang W. On the dynamics of a vaccination model with multiple transmission ways. International Journal of Applied Mathematics and Computer Science, 2013, 23(4):761-772
[14]	Zhou X, Cui J, Zhang Z. Global results for a cholera model with imperfect vaccination. Journal of the Franklin Institute, 2012, 301(3):770-791
[15]	Mwasa A, Tchuenche J M. Mathematical analysis of a cholera model with public health interventions. BioSystems, 2011, 105(3):190-200
[16]	Misra A K, Singh V. A delay mathematical model for the spread and control of water borne diseases. Journal of Theoretical Biology, 2012, 301:49-56
[17]	杨亚莉, 李建全, 刘万萌, 唐三一. 一类具有分布时滞和非线性发生率的媒介传染病模型的全局稳定性. 应用数学和力学, 2013, 34(12):1291-1299(Yang Y L, Li J Q, Liu W M, Tang S Y. Global stability of a vector-borne epidemic model with distributed delay and nonlinear incidence. Applied Mathematics and Mechanies, 2013, 34(12):1291-1299)
[18]	McCluskey C C. Complete global stability for an SIR epidemic model with delay-distributed or discrete. Nonlinear Analysis:Real World Applications, 2010, 11(6):55-59
[19]	Misra A K, Mishra S N, Pathak A L, Chandra P, Naresh R. Modeling the effect of time delay in controlling the carrier dependent infectious disease-Cholera. Applied Mathematics and Computation, 2012, 218(23):11547-11557
[20]	Gopalsamy K. Stability and Oscillations in Delay Differential Equations of Population Dynamics. Kluwer Academic, Dordrecht, Norwell, 1992
[21]	Hale J K. Theory of functional differential equations. New York:Spring-Verlag, 1977
[22]	Hassard BD, Kazarinoff ND, Wan YH. Theory and applications of Hopf bifurcation. Cambridge:Cambridge University Press, 1981
[23]	Hale J, Lunel S. Introduction to Functional Differential Equations. New York:Springer-Verlag, 1993

[1]	李敏, 赵东霞, 毛莉. 带有两个小世界联接的时滞环形神经网络系统的稳定性分析[J]. 应用数学学报, 2019, 42(1): 15-31.
[2]	李艳玲, 李瑜, 郭改慧. 一类混合比率依赖食物链扩散模型的Hopf分支[J]. 应用数学学报, 2019, 42(1): 1-14.
[3]	刘婷婷, 吴保卫, 刘丽丽, 王月娥. 离散切换正时滞系统在异步切换下的镇定性[J]. 应用数学学报, 2018, 41(6): 721-734.
[4]	刘永奇, 刘德林, 熊建栋. 具有离散时滞和Crowley-Martin功能性反应的HIV动力学模型稳定性研究[J]. 应用数学学报, 2018, 41(4): 461-472.
[5]	孟益民, 黄立宏, 郭上江. 具分布时滞双向联想记忆神经网络周期解的存在性及全局稳定性[J]. 应用数学学报, 2018, 41(3): 369-387.
[6]	刘炳文, 田雪梅, 杨孪山, 黄创霞. 具有非线性死亡密度和连续分布时滞的Nicholson飞蝇模型的周期解[J]. 应用数学学报, 2018, 41(1): 98-109.
[7]	王虎, 田晶磊, 孙玉琴, 于永光. 具有阶段结构的时滞分数阶捕食者-食饵系统的稳定性分析[J]. 应用数学学报, 2018, 41(1): 27-42.
[8]	孔丽丽, 李录苹. 具有不同时滞的两种捕食者-食饵恒化器模型的定性分析[J]. 应用数学学报, 2017, 40(5): 676-691.
[9]	赵环环, 刘有军, 燕居让. 带分布时滞偶数阶微分方程组的振动性[J]. 应用数学学报, 2017, 40(4): 612-622.
[10]	周辉, 王文, 周宗福. 具非线性收获项和S-型时滞Lasota-Wazewska模型的概周期解[J]. 应用数学学报, 2017, 40(3): 471-480.
[11]	赵才地, 阳玲, 刘国威, 许正雄. 一类时滞非牛顿流方程组在二维无界区域上的整体适定性与拉回吸引子[J]. 应用数学学报, 2017, 40(2): 287-311.
[12]	严勇. 一类含有最大值项的二元时滞积分不等式的推广[J]. 应用数学学报, 2017, 40(1): 85-98.
[13]	宋海涛, 刘胜强. 具有一般复发现象的疾病模型的全局稳定性[J]. 应用数学学报, 2017, 40(1): 37-48.
[14]	王琳. 具有多项式增长系数的随机延迟微分方程的整体解与矩估计[J]. 应用数学学报, 2016, 39(5): 765-785.
[15]	廖华英, 徐向阳, 胡启宙. 对"一类带收获率的离散时滞人口模型正周期解存在性"的探究[J]. 应用数学学报, 2016, 39(4): 598-609.

PDF全文下载地址:

http://123.57.41.99/jweb_yysxxb/CN/article/downloadArticleFile.do?attachType=PDF&id=14548