Global properties of infectious disease models with nonlinear incidence

被引：277

作者：

Korobeinikov, Andrei ^{[1
]}

机构：

[1] Hokkaido Univ, Res Inst Elect Sci, Lab Nonlinear Sci & Comp, Sapporo, Hokkaido 0600812, Japan

来源：

BULLETIN OF MATHEMATICAL BIOLOGY | 2007年 / 69卷 / 06期

基金：

日本学术振兴会;

关键词：

direct Lyapunov method; Lyapunov function; endemic equilibrium state; global stability; nonlinear incidence; 92D30; 34D20;

D O I：

10.1007/s11538-007-9196-y

中图分类号：

Q [生物科学];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

We consider global properties for the classical SIR, SIRS and SEIR models of infectious diseases, including the models with the vertical transmission, assuming that the horizontal transmission is governed by an unspecified function f(S,I). We construct Lyapunov functions which enable us to find biologically realistic conditions sufficient to ensure existence and uniqueness of a globally asymptotically stable equilibrium state. This state can be either endemic, or infection-free, depending on the value of the basic reproduction number.

引用

页码：1871 / 1886

页数：16

共 20 条

[11] The mathematics of infectious diseases [J].