GLOBAL STABILITY OF SIR EPIDEMIC MODELS WITH A WIDE CLASS OF NONLINEAR INCIDENCE RATES AND DISTRIBUTED DELAYS

被引：35
作者：
Enatsu, Yoichi [1 ]
Nakata, Yukihiko [2 ]
Muroya, Yoshiaki [3 ]
机构：
[1] Waseda Univ, Dept Pure & Appl Math, Shinjuku Ku, Tokyo 1698555, Japan
[2] Basque Ctr Appl Math, E-48160 Derio, Spain
[3] Waseda Univ, Dept Math, Shinjuku Ku, Tokyo 1698555, Japan
来源：
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B | 2011年 / 15卷 / 01期
基金：
日本学术振兴会;
关键词：
SIR epidemic models; nonlinear incidence rate; global asymptotic stability; permanence; distributed delays; Lyapunov functional; PERMANENCE;
D O I：
10.3934/dcdsb.2011.15.61
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we establish the global asymptotic stability of equilibria for an SIR model of infectious diseases with distributed time delays governed by a wide class of nonlinear incidence rates. We obtain the global properties of the model by proving the permanence and constructing a suitable Lyapunov functional. Under some suitable assumptions on the nonlinear term in the incidence rate, the global dynamics of the model is completely determined by the basic reproduction number R-0 and the distributed delays do not influence the global dynamics of the model.
引用
收藏
页码：61 / 74
页数：14
相关论文
共 22 条
[1]   POPULATION BIOLOGY OF INFECTIOUS-DISEASES .1. [J].
ANDERSON, RM ;
MAY, RM .
NATURE, 1979, 280 (5721) :361-367
[2]  
[Anonymous], 1961, STABILITY LYAPUNOVS
[3]   Convergence results in SIR epidemic models with varying population sizes [J].
Beretta, E ;
Takeuchi, Y .
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1997, 28 (12) :1909-1921
[4]  
BROWN GC, 1995, J INVERTEBR PATHOL, V65, P10, DOI 10.1006/jipa.1995.1002
[5]   GENERALIZATION OF THE KERMACK-MCKENDRICK DETERMINISTIC EPIDEMIC MODEL [J].
CAPASSO, V ;
SERIO, G .
MATHEMATICAL BIOSCIENCES, 1978, 42 (1-2) :43-61
[6]  
Cooke K.L., 1979, The Rocky Mountain Journal of Mathematics, V9, P31, DOI [DOI 10.1216/RMJ-1979-9-1-31, 10.1216/RMJ-1979-9-1-31]
[7]  
Hale J.K., 1993, Introduction to Functional Differntial Equations
[8]  
HETHCOTE H W, 1976, Mathematical Biosciences, V28, P335, DOI 10.1016/0025-5564(76)90132-2
[9]   The mathematics of infectious diseases [J].
Hethcote, HW .
SIAM REVIEW, 2000, 42 (04) :599-653
[10]   Global Stability for Delay SIR and SEIR Epidemic Models with Nonlinear Incidence Rate [J].
Huang, Gang ;
Takeuchi, Yasuhiro ;
Ma, Wanbiao ;
Wei, Daijun .
BULLETIN OF MATHEMATICAL BIOLOGY, 2010, 72 (05) :1192-1207
123