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潜伏期和染病期均传染的SEIS模型的分析 被引量：2

Analysis of SEIS epidemic model with transmission in both latent period and infected period
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摘要 研究了潜伏期和染病期均传染的SEIS模型.给出了各类平衡点存在的条件阈值,证明了无病平衡点全局渐近稳定性的条件,并且利用第二加性复合矩阵给出了地方平衡点的存在性和全局渐近稳定性的充分条件. A kind of SEIS epidemic models with transmission in both latent period and infected period was studied.The threshold for the existence condition of all kinds of equilibriums were identified,the global asymptotic stability of disease-free equilibrium was proved,and the sufficient condition for the existence and the global asymptotic stability of the endemic equilibrium point was also proved by use of the second compound matrix.
作者 赵海全 王美娟 唐春婷
机构地区 上海理工大学理学院
出处 《上海理工大学学报》 CAS 北大核心 2010年第5期457-460,共4页 Journal of University of Shanghai For Science and Technology
关键词 流行病模型 平衡点 全局渐近稳定性 复合矩阵 epidemic model equilibrium global asymptotic stability compound matrix
分类号 O175.13 [理学—基础数学]
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参考文献6

  • 1原三领,韩丽涛,马知恩.一类潜伏期和染病期均传染的流行病模型[J].生物数学学报,2001,16(4):392-398. 被引量：54
  • 2THIEME H R. Persistence under relaxed point-dissipativity with applications to an epidemic model[J]. Mathematical Analysis, 1993,24(2) :407 - 435.
  • 3LI M Y, MULDOWNEY J S. A geometric approach to global-stability problems[J]. Mathematical Analysis, 1996,27(2) 1 070- 1 083.
  • 4LI M Y, WANG L C. Global stability in some SEIR epidemic models[J]. Institute of Mathematics and Its Applications, 2002,126 : 295 - 311.
  • 5MULDOWNEY J S. Compound matrices and ordinary differential equations[J].Rocky Mount J Math, 1990,20 (4)857 - 872.
  • 6MARTIN J R H. Logarithmic norms and projections applied to linear differential systems[J].Mathematical Analysis and Applications, 1974,45 (2) : 432 - 454.

二级参考文献7

  • 1[1]Kermark M D. Mokendrick A G. Contributions to the mathematical theory of epidemics[J]. Part I, Proc Roy Soc, A, 1927, 115(5):700-721.
  • 2[2]Cooke K L. Stability analysis for a vector disease model[J]. Rocky Mount J Math, 1979, 9(1):31-42.
  • 3[3]Hethcote H W. Qualititative analyses of communicable disease models[J]. Math Biosci, 1976, 28(3):335-356.
  • 4[4]Capasso V. Mathematical structures of epidemic systems[J]. Lecture notes in biomath[M]. 97 Springer-verlag,1993.
  • 5[5]Hethcote H W, Liu W M, Leven S A. Dynamical behavior of epidemiological models with nonlinear incidence rates[J]. Math Biosci, 1987, 25(3):359-380.
  • 6[6]Capasso V, Serio G. A generalization of the Kermack-Mckendrick deterministic epidemic model[J]. Math Biosci, 1978, 42(1):41-61.
  • 7[7]Bailey N T J. The Mathematical Theorey of Infectious Diseases.[M]. London: Griffin, 1975.

共引文献53

同被引文献16

  • 1Li M Y, Muldowney J S. Global stability for the SEIR model in epidemiology[J]. Math Biosei, 1995, 125: 155-64.
  • 2Li M Y, Muldowney J S. A geometric approach to the global-stability problems[J]. SIAM J Math Anal, 1996, 27; 1070-83.
  • 3Li M Y, Graef J R, Wang L C, Karsai J. Global dynamics of a SEIR model with a varying total population size [J]. Math Biosci, 1999, 160: 191- 213.
  • 4Fan M, Li M Y. Global stability o{ an SEIS epidemic model with recruitment and a varying total population size[J]. Math Biosci, 2001, 170: 199-208.
  • 5Li M Y, Wang L. Global stability in some SEIR epidemic models IMA, 126: 295-311.
  • 6Guihua Li, Jin Zhen, Global stability of an SEI epidemic model with general contact rate[J]. Chaos, Solitons and Fractals, 2005(23): 997-1004.
  • 7Guihua Li, Wendi Wang, Zhen Jin. Global stability of an SEIR epidemic model with constant immigration [J]. Chaos, Solitons and Fractals, 2006 (30) : 1012- 1019.
  • 8Hethcote H. The mathematics of infectious diseases [J]. SIAM Review, 2000(42): 599.
  • 9方彬,杨金根,李学志.潜伏期和染病期均具有康复的年龄结构MSEIS流行病模型的稳定性[J].应用数学,2009,22(1):90-100. 被引量：4
  • 10张改平,董玉才,许飞,张欢.具有垂直传染且总人口在变化的SIRS传染病模型的渐近分析[J].数学的实践与认识,2011,41(18):139-143. 被引量：2

引证文献2

上海理工大学学报
2010年 第5期

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