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一类带有种痘的齐次SIR传染病模型分析 被引量：3

Analysis of a homogeneous SIR epidemic model with vaccination
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摘要 讨论了一类带有种痘的齐次SIR模型,利用齐次系统理论研究了该模型平衡点的稳定性.结果表明:当基本再生数R(ψ)<1时,无病平衡点局部渐近稳定;当R(ψ)>1时,无病平衡点不稳定,同时得到了地方病平衡点稳定性的充分条件. This paper considers an age-structured homogeneous SIR model with vaccination. The stability of the equilibria for this model is investigated by using the theory of homogeneous dynamics system. The results show that the disease free equilibrium is stable if the threshold parameter is less than 1. If the threshold parameter is more than 1, the disease free equilibrium is unstable. An explicit sufficient condition for the stability of endemic equilibrium is obtained.
作者 郭淑利 姚峰
机构地区 信阳师范学院数学与信息科学学院 南阳医学高等专科学校
出处 《信阳师范学院学报（自然科学版）》 CAS 北大核心 2005年第4期376-380,共5页 Journal of Xinyang Normal University(Natural Science Edition)
基金 河南省自然科学基金资助项目(0511012800)
关键词 SIR模型 齐次方程 C0-半群 谱 平衡态 稳定性 SIR model homogeneous equations C0-semigroup spectrum equilibrum stability
分类号 O175 [理学—基础数学]
  • 相关文献

参考文献14

  • 1LI MICHAEL Y,SMITH HAL L,WANG Liancheng.Global dynamics of an SEIR epidemic model with vertical transmission[J].SIAM APPL Math,2001,62(1):58-69.
  • 2娄洁,马知恩.一类有被动免疫的流行病模型研究[J].数学物理学报（A辑）,2003,23(3):357-368. 被引量：13
  • 3CHA Youngjoon, IANNELLI M,MILNER F A.Stability of change of an epidemic model [J].Dynamic System Appl,2000, 9:361-376.
  • 4FENG Z,IANNELLI M,MILNER F A.A two-strain tuberculosis model with age of infection [J].SIAM Math,2002, 62(5): 1634-1656.
  • 5MARTCHEVA Maia, CASTILLO-CHAVEZ Carlos.Disease with chronic stage in a population with varing size[J].Math Biosciences,2003, 182: 1-25.
  • 6HADELER K.Pair formation with maturation period [J]. Math Biol,1993,32: 1-15.
  • 7HADELER K.Periodic solutions of homogeneuous equations[J].Diff Eq,1992, 95: 183-202.
  • 8HADELER K,WALDSTTTER R, WRZ-BUSEKROS A.Models for pair formation in bisexual populations[J].Math Biol,1988, 26: 635-649.
  • 9FREDRICHSON A.A mathematical theory of age structure in sexual population:random mating and monogamous marriage models [J].Math Biosci,1971, 10: 117-143.
  • 10HOPPENSTEADT F.Mathematical theories of populations: demographics, genetics and epidemics society for industrial and applied mathematics[M]. Philadelphia,1975.

二级参考文献10

  • 1Capasso V. Mathematical Structures of Epidemic Systems. Berlin: Springer-Verlay, 1993. Vol. 97 of lecture notes in Biomathematics.
  • 2Chen L, Chen J. Nonlinear Dynamical Systems of Biology. Beijing: Academic Press, 1993.
  • 3Anderson R M, May R M. Population biology of infectious diseases I. Nature, 1979,180:361-367.
  • 4Li M Y, Graef j R, Wang L, Karsai J. Global dynamics of an SEIR model with varying population size. Math Biosci, 1999,160:191-213.
  • 5Hethcote H W. The Mathematics of Infectious Disease. SIAM REVIEW 2000, 42(4):599-653.
  • 6Gao L Q, Hethcote H W. Disease transmission models with density-dependent demographics. J Math Biol, 1992,30:717-731.
  • 7Hethcote H W, Stech H W, P Van Den Driessche. Periodicity and stability in epidemic models. In: Busenberg S N, Cooke K L, edt. Differential Equations and Applications in Ecology, Epidemic and Population Problems. New York: Academic Press, 1981. 65-82.
  • 8Schuette M C, Hethcote H W. Modelling the effects of varicella vaccination programs on the incidence of chickenpox and shingles. Bull Math Biol, 1999, 61:1031-1064.
  • 9Thieme H R. Persistence under relaxed point-dissipativity. SIAM J Math Anal, 1993, 24:407-435.
  • 10Smith H L, Waltman P. Perturbation faglobally stable steady state. Proceedings of the American Mathematical Society, 1999, 127: 447-453.

共引文献12

同被引文献20

  • 1李学志,万志超,陈清江.总人口规模变化的年龄结构MSEIR流行病模型的再生数[J].数学的实践与认识,2005,35(8):113-122. 被引量：2
  • 2李学志,代丽霞.总人口规模变化的年龄结构SEIR流行病模型的稳定性[J].系统科学与数学,2006,26(3):283-300. 被引量：7
  • 3Li Xue - Zhi, Geni Gupur. Global Stability of an Age - structured SIRS Epidemic Model with Vaccination [ J ]. Discrete and Continuous Dynamical Systems -Series B, 2004,4(3) :643 -652.
  • 4Shim E, Feng Z, Martcheva M. An Age - structured Epidemic Model of Rotavirus with Vaccination [ J ]. Math Biol,2006,53:719 - 746.
  • 5ANDREASEN V,PUGLIESE A.Pathogen Coexistence Induced by Density Dependent Host Mortality[J].Theor Biol(S 0022-5193),1995,177:159-165.
  • 6FENG Z,IANNELLI M,MILNER F A.A Two-strain Tuberculosis Model with Age of Infection SIAM[J].Appl Math(S 0036-1399),2002,62:1634-1656.
  • 7ACKLEH A S,ALLEN L J S.Competitive Exclusion in SIS and SIR Epidemic Models with Total cross Immunity and Density-dependent Host Mortality[J].Discrete and Continuous Dynamical Systems-Series B(S 1531-3492),2005,5:175-188.
  • 8VAN P,DRIESSCHE D,WATMOUGH J.Reproduction Numbers and Sub-threshold Endemic Equilibria for Compartmental Models of Disease Transmission[J].Math Biosci(S 0025-5564),2002,180:29-48.
  • 9ACKLEH A S,ALLEN L J S.Competitive Exclution and Coexistence for Pathogens in an Epidemic Model with Variable Population size[J].Math Biol(S 0303-6812),2003,47:153-168.
  • 10CASTILLO-CHAVEZ C,HUANG W,LI J.Competitive Exclusion and Coexistence of Multiple Strains in an SIS STD Model SIAM[J].Appl Math(S 0036-1399),1999,59:1790-1811.

引证文献3

二级引证文献4

信阳师范学院学报（自然科学版）
2005年 第4期

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