|本期目录/Table of Contents|

一类具年龄结构非自治传染病模型零平衡解的全局渐近稳定性(PDF)

《内蒙古大学学报(自然科学版)》[ISSN:1000-9035/CN:22-1262/O4]

期数:
2011年01期
页码:
1-11
栏目:
研究论文
出版日期:
2011-01-20

文章信息/Info

Title:
Global Asymptotic Stability of the Zero Equilibrium Solution for a Class of Non-autonomous Epidemic Model with Age Structure
作者:
陈林1 闫萍23
1. 伊犁师范学院数学系, 新疆 伊宁 835000;
2. 安徽农业大学理学院, 合肥 230036;
3. 新疆大学数学与系统科学学院, 乌鲁木齐 830046
Author(s):
CHEN Lin1 YAN Ping23
1. Department of Mathematics,Yili Normal University,Yining 835000,China;
2. School of Science,Anhui Agricultural University,Hefei 230036,China;
3. College of Mathematics and Systems Science,Xinjiang University,Urumqi 830046,China
关键词:
年龄结构病程稳定性基本再生数存在唯一性
Keywords:
age-structureinfection agestabilitybasic reproductive numberexistence and uniqueness
分类号:
O175
DOI:
-
文献标识码:
-
摘要:
建立了一类具有年龄结构和病程结构的传染病模型(SIS).分析了具有构造性迭代序列的模型的全局动力学性态并计算出了基本再生数R0.具体说明了基本再生数R0对整个动力学性态起到的阈值作用.也就是说,当R0<1时,零平衡解是全局渐近稳定的,当R0>1时,零平衡解是不稳定的,此时具有唯一的正平衡解.
Abstract:
A general SIS model with chronological age and infection age structure is formulated.The global dynamic behavious of the model with a constructive iteration procedure are analyzed.The base productive number R0 is calculated by using the next generation operator approach.It is showed that R0 plays a sharp threshold role in determining the global dynamic behavious,i.e.,the zero equilibrium solution is globally asymptotically stable if R0 1,while the zero equilibrium solution is unstable and exists a unique positive equilibrium solution if R01.

参考文献/References

[1] Viggo Andreasen,Thomas Fromelt. A school-oriented,age-structured epidemic model[J].SIAM Journal on Applied Mathematics,2005,(06):1870-1887.
[2] 马知恩,周义仓,王稳地. 传染病动力学的数学建模与研究[M].北京:科学出版社,2004.
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[5] Maia Martcheva,Sergel S.Plyugin. The role of coinfection in multidisease dynamics[J].SIAM Journal on Applied Mathematics,2006,(03):843-872.
[6] 黄怡. 具年龄结构和病程结构的传染病偏微分模型[J].新疆大学学报(自然科学版),2009,(02):159-163.
[7] Busenberg S,Castillo-Chavez C. A general solution of the problem of mixing of subpopulations and its application to risk-and age-structured epidemic models for the spread of AIDS[J].IMA Journal of Mathematics Applied in Medicine and Biology,1990.1-29.
[8] Zhou Yicang,Song Baojun,Ma Zhien. The global stability analysis for a SIS model with age and infection age structures[A].Beilin:Springer-Verlag,2001.313-335.
[9] 陈林,闫萍,盛其荣. 一类具有年龄结构非自治种群模型零平衡解的全局渐近稳定性[J].内蒙古大学学报(自然科学版),2009,(03):241-246.

备注/Memo

备注/Memo:
收稿日期:2009-11-9;改回日期:。
基金项目:伊犁师范学院2009年度科研计划资助项目(2009-34);新疆高校科研计划重点资助项目(XJEDU2007I03)
作者简介:陈林(1978-),男,新疆伊宁市人,讲师,理学硕士,研究方向:偏微分方程及其应用.
更新日期/Last Update: 1900-01-01