QUALITATIVE ANALYSIS AND TRAVELLING WAVE SOLUTIONS FOR THE SI MODEL WITH VERTICAL TRANSMISSION

被引：43
作者：
Ducrot, Arnaud [1 ]
Langlais, Michel [1 ]
Magal, Pierre [1 ]
机构：
[1] Univ Bordeaux 2, INRIA Bordeaux Sud Ouest, EPI Anubis,CNRS,UMR 5251, UFR Sci & Modelisat,Inst Math Bordeaux, F-33076 Bordeaux, France
来源：
COMMUNICATIONS ON PURE AND APPLIED ANALYSIS | 2012年 / 11卷 / 01期
关键词：
Spatially structured SI model; global stability; travelling wave solutions;
D O I：
10.3934/cpaa.2012.11.97
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this note we analyze a spatially structured SI epidemic model with vertical transmission, a logistic effect on vital dynamics and a density dependent incidence. For a bounded spatial domain we show global stability of the endemic state when it is feasible. Then we look at the existence of travelling wave solutions connecting the endemic and the disease free states.
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页码：97 / 113
页数：17
相关论文
共 21 条
  • [1] [Anonymous], 1937, Bull. Univ. Mosc. Ser. Int. A, DOI DOI 10.1016/B978-0-08-092523-3.50014-9
  • [2] Harnack's inequality for cooperative weakly coupled elliptic systems
    Arapostathis, A
    Ghosh, MK
    Marcus, SI
    [J]. COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 1999, 24 (9-10) : 1555 - 1571
  • [3] Brauer F., 2000, Mathematical Models in Population Biology and Epidemiology
  • [4] Busenberg S., 1993, BIOMATHEMATICS
  • [5] Capasso V., 1993, Mathematical Structure of Epidemic Systems, DOI DOI 10.1007/978-3-540-70514-7
  • [6] Harnack principle for weakly coupled elliptic systems
    Chen, ZQ
    Zhao, Z
    [J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 1997, 139 (02) : 261 - 282
  • [7] Diekmann O., 2000, Mathematical epidemiology of infectious diseases: model building, analysis and interpretation
  • [8] The wave of advance of advantageous genes
    Fisher, RA
    [J]. ANNALS OF EUGENICS, 1937, 7 : 355 - 369
  • [9] Fitzgibbon WE, 2008, LECT NOTES MATH, V1936, P115
  • [10] Fitzgibbon W.E., 2003, COMMUNICATIONS APPL, V7, P387
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