Permanence of an SIR epidemic model with distributed time delays

被引：93
作者：
Ma, WB
Takeuchi, Y
Hara, T
Beretta, E
机构：
[1] Univ Sci & Technol Beijing, Dept Math & Mech, Beijing 100083, Peoples R China
[2] Shizuoka Univ, Dept Syst Engn, Fac Engn, Hamamatsu, Shizuoka 4328561, Japan
[3] Univ Osaka Prefecture, Dept Math Sci, Sakai, Osaka 5998531, Japan
[4] Univ Urbino, Ist Biomatemat, I-61029 Urbino, Italy
来源：
TOHOKU MATHEMATICAL JOURNAL | 2002年 / 54卷 / 04期
关键词：
epidemic model; time delay; permanence;
D O I：
10.2748/tmj/1113247650
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We consider permanence of an SIR epidemic model with distributed time delays. Based on some known techniques on limit sets of differential dynamical systems, we show that, for any time delay, the SIR epidemic model is permanent if and only if an endemic equilibrium exits.
引用
收藏
页码：581 / 591
页数：11
相关论文
共 14 条
[1]   POPULATION BIOLOGY OF INFECTIOUS-DISEASES .1. [J].
ANDERSON, RM ;
MAY, RM .
NATURE, 1979, 280 (5721) :361-367
[2]   Global asymptotic stability of an SIR epidemic model with distributed time delay [J].
Beretta, E ;
Hara, T ;
Ma, WB ;
Takeuchi, Y .
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2001, 47 (06) :4107-4115
[3]  
BERETTA E, 1995, J MATH BIOL, V33, P250, DOI 10.1007/BF00169563
[4]   GLOBAL STABILITY RESULTS FOR A GENERALIZED LOTKA-VOLTERRA SYSTEM WITH DISTRIBUTED DELAYS - APPLICATIONS TO PREDATOR-PREY AND TO EPIDEMIC SYSTEMS [J].
BERETTA, E ;
CAPASSO, V ;
RINALDI, F .
JOURNAL OF MATHEMATICAL BIOLOGY, 1988, 26 (06) :661-688
[5]   UNIFORMLY PERSISTENT SYSTEMS [J].
BUTLER, G ;
FREEDMAN, HI ;
WALTMAN, P .
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1986, 96 (03) :425-430
[6]  
COOKE K. L., 1979, Rocky Mountain Journal of Mathematics, V9, P31, DOI DOI 10.1216/RMJ-1979-9-1-31
[7]   UNIFORM PERSISTENCE IN FUNCTIONAL-DIFFERENTIAL EQUATIONS [J].
FREEDMAN, HI ;
RUAN, SG .
JOURNAL OF DIFFERENTIAL EQUATIONS, 1995, 115 (01) :173-192
[8]  
HALANAY A, 1969, DIFFERENTIAL EQUATIO
[9]  
Hale J. K., 1977, Applied Mathematical Sciences, V3
[10]   PERSISTENCE IN INFINITE-DIMENSIONAL SYSTEMS [J].
HALE, JK ;
WALTMAN, P .
SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 1989, 20 (02) :388-395
12