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具有一般非线性接触率及潜伏年龄结构的SEIS传染病模型稳定性分析 被引量:1

Stability Analysis of SEIS Epidemic Model with Latent Age Dependent and Generally Nonlinear Contact Rate
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摘要 讨论一类具有一般非线性接触率及潜伏年龄结构的SEIS传染病模型,研究了地方病平衡点的存在性、无病平衡点的全局稳定性以及地方病平衡点的指数稳定性,得到地方病平衡点指数稳定的一般性条件. The existence of endemic equilibrium and the global stability of desease free equilibrium of a SEIS epidemic model with generally nonlinear contact rate and latent age dependent are discussed.In the sequal,an ordinary condition is obtained,and which assures the endemic equilibrium is exponentially stable.
出处 《上海大学学报(自然科学版)》 CAS CSCD 北大核心 2011年第5期636-641,共6页 Journal of Shanghai University:Natural Science Edition
基金 国家自然科学基金资助项目(10971064) 国家自然科学基金数学天元基金资助项目(11026133) 中国博士后基金资助项目(20090461281) 陕西省教育厅专项科研计划资助项目(11JK0531) 西安科技大学培育基金资助项目(2010042)
关键词 SEIS传染病模型 非线性接触率 平衡点 潜伏年龄结构 渐近稳定性 SEIS epidemic model nonlinear contact rate equilibrium latent age dependent asymptotically stable
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参考文献10

  • 1THIEME H R, CASTILLO-CHAVEZ C. How may infectionage-dependent infectivity affect the dynamics of HIV/ AIDS? [ J ]. SIAM J Appl Math, 1993, 53 (5) : 1447- 1479.
  • 2KIN M Y, MILNER F A. A mathematical model of epidemics with screening and variable infectivity [ J ]. Math Comput Modelling, 1995, 21(7):29-42.
  • 3KIM M Y. Existence of steady state solutions to an epidemic model with screening and their asymptotic stability [J]. Appl Math Comput, 1996, 74(1) :37-58.
  • 4KRIBS-ZALETA C M, MARTCHEVA M. Vaccination strategies and backward bifurcation in an age-since-infection structured model [J]. Math Biosci, 2002, 177/178(2):317-332.
  • 5INABA H, SEKINE H. A mathematical model for Chagas disease with infection-age-dependent infectivity [ J ]. Math Biosci, 2004, 190(4) :39-69.
  • 6LI J, ZHOU Y C, MA Z Z, et al. Epidemiological models for mutating pathogens [ J]. SIAM J Appl Math, 2004, 65 ( 1 ) : 1-23.
  • 7徐文雄,张仲华.年龄结构SIR流行病传播数学模型渐近分析[J].西安交通大学学报,2003,37(10):1086-1089. 被引量:30
  • 8ZHANG Z H, PENG J G. A SIRS epidemic model with infection-age dependence [J]. J Math Anal Appl, 2007, 331 (2) :1396-1414.
  • 9张仲华,徐文雄.一类SEIS流行病传播数学模型的渐近分析[J].陕西师范大学学报(自然科学版),2004,32(3):1-3. 被引量:2
  • 10王拉娣,李建全.一类带有非线性传染率的SEIS传染病模型的定性分析[J].应用数学和力学,2006,27(5):591-596. 被引量:22

二级参考文献24

  • 1徐文雄,CarlosCastillo-Chavez.一个积分-微分方程模型解的存在唯一性(英文)[J].工程数学学报,1998,15(2):108-112. 被引量:9
  • 2陈兰荪.数学生态学模型与研究方法[M].北京:科学出版社,1998..
  • 3Thieme H R, Castillo-Chavez C. How may infection age-dependent infectivity affect the dynamics of HIV/AIDS? [J]. Siam J Appl Math, 1993, 53(5): 1 447-1 479.
  • 4Feng Z, Iannelli M, Milner F A. A two-strain tuberculosis model with age of infection [J]. Siam J Appl Math, 2002,62(5):1 634-1 656.
  • 5Castillo-Chavez C, Feng Zhilan.Global stability of an age structure model for TB and its applications to optional vaccination strategies [J]. Mathematical Biosciences, 1998, 151(2):135-154.
  • 6Xiao Yanni, Chen Lansun, Bosch F V D. Dynamical behavior for a stage-structured SIR infectious disease model [J]. Nonlinear Analysis: Real World Applications, 2002, 3(2):175-190.
  • 7Song Baojun, Castillo-Chavez C, Aparicio J P. Tuberculosis models with fast and slow dynamics: the role of close and casual contacts [J]. Mathematical Biosciences, 2002, 180(1/2): 187-205.
  • 8Kermark M D, Mckendrick A G. Contributions to the mathematical theory of epidemics[J]. Proceeding of the Royal Society of London, Series A, Physical and Engineering Sciences, 1927, 115(5): 700-721.
  • 9Horst R Thieme, Carlos Castillo-Chavez. How may infection age-dependent in festivity affect the dynamics of HIV/AIDS? [J ]. Society for Industrial and Applied Mathematics Journal Mathematics, 1993, 53 (5): 1447~1479.
  • 10陈兰荪.数学生态学模型与研究方法[M].北京:科学出版社,1998..

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