LYAPUNOV FUNCTIONS AND GLOBAL STABILITY FOR SIR AND SEIR MODELS WITH AGE-DEPENDENT SUSCEPTIBILITY

被引：40
|
作者：
Melnik, Andrey V. [1 ]
Korobeinikov, Andrei [2 ]
机构：
[1] OCCAM, Math Inst, Oxford OX1 3LB, England
[2] Ctr Recerca Matemat, Barcelona 08193, Spain
来源：
MATHEMATICAL BIOSCIENCES AND ENGINEERING | 2013年 / 10卷 / 02期
基金：
爱尔兰科学基金会;
关键词：
Infectious disease; endemic equilibrium state; global stability; direct Lyapunov method; Lyapunov function; compartment model; age structure; age structured model; distributed population model; ASYMPTOTIC PROPERTIES; DYNAMICS; INFECTION; DELAY;
D O I：
10.3934/mbe.2013.10.369
中图分类号：
Q [生物科学];
学科分类号：
07 ; 0710 ; 09 ;
摘要：
We consider global asymptotic properties for the SIR and SEIR age structured models for infectious diseases where the susceptibility depends on the age. Using the direct Lyapunov method with Volterra type Lyapunov functions, we establish conditions for the global stability of a unique endemic steady state and the infection-free steady state.
引用
收藏
页码：369 / 378
页数：10
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