一类新的含有垂直传染与脉冲免疫的时滞SEIR传染病模型的全局动力学行为

孟新柱; 陈兰荪; 宋治涛

一类新的含有垂直传染与脉冲免疫的时滞SEIR传染病模型的全局动力学行为

1.
山东科技大学理学院,山东青岛 266510;2.大连理工大学应用数学系,辽宁大连 116024

基金项目: 国家自然科学基金资助项目(10471117)

详细信息

作者简介:
孟新柱(1972- ),男,山东定陶人,博士,副教授,从事生物数学研究(联系人.E-mail:mxz721106@sdust.edu.cn).

中图分类号: O175
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出版历程
- 收稿日期: 2007-01-23
- 修回日期: 2007-04-16
- 刊出日期: 2007-09-15

Global Dynamics Behaviors for a New Delay SEIR Epidemic Disease Model With Vertical Transmission and Pulse Vaccination

1.
College of Science, Shandong University of Science and Technology, Qingdao 266510, P. R. China;

摘要

摘要: 对一个带有有害时滞与垂直传染的SEIR传染病模型,在脉冲免疫接种条件下，分析了其动力学行为．运用离散动力系统的频闪映射,获得了一个‘无病’周期解,证明了当模型的一些参数在适当的条件下,该‘无病’周期解是全局吸引的．运用脉冲时滞泛函微分方程理论,获得了含有时滞的持久性的充分条件,并且证明了时滞、脉冲免疫与垂直传染对模型的动力学行为能够产生显著的影响．结论表明该时滞是“有害”时滞．
- 持久性 /
- 脉冲免疫接种 /
- 水平与垂直传染 /
- 时滞 /
- 全局吸引性
Abstract: A robust SEIR epidemic disease model with a profitless delay and vertical transmission was formulated, and the dynamics behaviors of the model under pulse vaccination were analyzed. By use of the discrete dynamical system determined by the stroboscopic map, an infection-free. periodic solution was obtained. Further, it is shown that the infection-free. periodic solution is globally attractive when some parameters of the model are under appropriate conditions. Using the theory on delay functional and impulsive differential equation, sufficient condition with time delay for the permanence of the system was obtained. And it was proved, that time delays, pulse vaccination and vertical transmission can bring obvious effects on the dynamics behaviors of the model. The results indicate that the delay is "profitless".
- permanence /
- pulse vaccination /
- horizontal and vertical transmission /
- delay /
- global attractivity

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参考文献(28)

[1]	Michael Y Li,Gaef John R,WANG Lian-cheng,et al.Global dynamics of an SEIR model with varying total population size[J].Mathematical Biosciences,1999，160(2):191-213. doi: 10.1016/S0025-5564(99)00030-9
[2]	Michael Y Li,Hall Smith,Wang Lian-cheng.Global dynamics of an SEIR epidemic model with vertical transmission[J].SIAM Journal on Applied Mathematics,2001，62(1):58-69. doi: 10.1137/S0036139999359860
[3]	Al-Showaikh F N M,Twizell E H.One-dimensional measles dynamics[J].Applied Mathematics and Computation,2004，152(1):169-194. doi: 10.1016/S0096-3003(03)00554-X
[4]	Greenhalgh D.Hopf bifurcation in epidemic models with a latent period and nonpermanent immunity[J].Mathematical and Computer Modelling,1997，25(5):85-107.
[5]	LI Gui-hua,JIN Zhen.Global stability of an SEIR epidemic model with infectious force in latent,infected and immune period[J].Chaos, Solitons and Fractals,2005，25(5):1177-1184. doi: 10.1016/j.chaos.2004.11.062
[6]	Hethcote H W,Stech H W,Van den Driessche P.Periodicity and stability in epidemic models: A survey[A].In:Differential Equations and Applications in Ecology,Epidemics,and Population Problems[M].New York:Academic Press,1981,65-85.
[7]	D'Onofrio Alberto.Stability properties of pulse vaccination strategy in SEIR epidemic model[J].Mathematical Biosciences,2002，179(1):57-72. doi: 10.1016/S0025-5564(02)00095-0
[8]	D'Onofrio Alberto. Mixed pulse vaccination strategy in epidemic model with realistically distributed infectious and latent times[J].Applied Mathematics and Computation,2004，151(1):181-187. doi: 10.1016/S0096-3003(03)00331-X
[9]	Fine P M.Vectors and vertical transmission: an epidemiologic perspective[J].Annals of the New York Academy of Sciences,1975，266(11):173-194. doi: 10.1111/j.1749-6632.1975.tb35099.x
[10]	Busenberg S,Cooke K L,Pozio M A.Analysis of a model of a vertically transmitted disease[J].Journal of Mathematical Biology,1983，17(3):305-329.
[11]	Busenberg S N,Cooke K L.Models of vertical transmitted diseases with sequenty-continuous dynamics[A].In:Lakshmicantham V Ed.Nonlinear Phenomena in Mathematical Sciences[C].New York:Academic Press,1982,179-187.
[12]	Cook K L,Busenberg S N.Vertical transmission diseases[A].In:Lakshmicantham V Ed.Nonlinear Phenomena in Mathematical Sciences[C].New York:Academic Press,1982,189.
[13]	LU Zhong-hua,CHI Xue-bin,CHEN Lan-sun.The effect of constant and pulse vaccination on SIR epidemic model with horizontal and vertical transmission[J].Mathematical and Computer Modelling,2002，36(9):1039-1057. doi: 10.1016/S0895-7177(02)00257-1
[14]	D'Onofrio Alberto. On pulse vaccination strategy in the SIR epidemic model with vertical transmission[J].Applied Mathematics Letters,2005，18(7):729-732. doi: 10.1016/j.aml.2004.05.012
[15]	Nokes D, Swinton J.The control of childhood viral infections by pulse vaccination[J].IMA Journal Mathematics Applied Biology Medication,1995，12(1):29-53. doi: 10.1093/imammb/12.1.29
[16]	ZENG Guang-zhao,CHEN Lan-sun.Complexity and asymptotical behavior of an SIRS epidemic model with proportional implse vaccination[J].Advances in Complex Systems,2005，8(4):419-431. doi: 10.1142/S0219525905000580
[17]	Van den Driessche P,Watmough J.A simple SIS epidemic model with a backward bifurcation[J].Journal of Mathematical Biology,2000，40(6):525-540. doi: 10.1007/s002850000032
[18]	Van den Driessche P, Watmough J. Epidemic solutions and endemic catastrophes[J].Fields Institute Communications,2003，36(1):247-257.
[19]	Alexander M E,Moghadas S M.Periodicity in an epidemic model with a generalized non-linear incidence[J].Mathematical Biosciences,2004，189(1):75-96. doi: 10.1016/j.mbs.2004.01.003
[20]	Takeuchi Yasuhiro,MA Wan-biao,Beretta Edoardo. Global asymptotic properties of a delay SIR epidemic model with finite incubation times[J].Nonlinear Analysis,2000，42(6):931-947. doi: 10.1016/S0362-546X(99)00138-8
[21]	MA Wan-biao,SONG Mei,Takeuchi Yasuhiro.Global stability of an SIR epidemic model with time delay[J].Applied Mathematics Letters,2004,17(10):1141-1145. doi: 10.1016/j.aml.2003.11.005
[22]	JIN Zhen,MA Zhi-en.The stability of an SIR epidemic model with time delays[J].Mathematical Biosciences and Engineering,2006,3(1):101-109.
[23]	Beretta Edoardo,Hara Tadayuki,MA Wang-bao,et al.Global asymptotic stability of an SIR epidemic model with distributed time delay[J].Nonlinear Analysis,2001,47(6):4107-4115. doi: 10.1016/S0362-546X(01)00528-4
[24]	Lakshmikantham V,Bainov D,Simeonov P.Theory of Impulsive Differential Equations[M].Singapore:World Scientic,1989.
[25]	LIU Xin-zhi,Teo Kok Lay,ZHANG Yi.Absolute stability of impulsive control systems with time delay[J].Nonlinear Analysis,2005，62(3):429-453. doi: 10.1016/j.na.2005.03.052
[26]	KUANG Yang.Delay Differential Equations with Applications in Population Dynamics[M].San Diego, CA:Academic Press,Inc.1993.
[27]	Cooke K L, Van den Driessche P. Analysis of an SEIRS epidemic model with two delays[J].Journal of Mathematical Biology,1996，35(2):240-260. doi: 10.1007/s002850050051
[28]	WANG Wen-di.Global Behavior of an SEIRS epidemic model with time delays[J].Applied Mathematics Letters,2002,15(4):423-428. doi: 10.1016/S0893-9659(01)00153-7