GLOBAL ASYMPTOTIC PROPERTIES OF STAGED MODELS WITH MULTIPLE PROGRESSION PATHWAYS FOR INFECTIOUS DISEASES

被引：10

作者：

Melnik, Andrey V. ^{[1
]}

Korobeinikov, Andrei ^{[2
]}

机构：

[1] Samara Nayanova Acad, Dept Appl Math & Comp Sci, Samara 443001, Russia

[2] Univ Limerick, MACSI, Dept Math & Stat, Limerick, Ireland

来源：

MATHEMATICAL BIOSCIENCES AND ENGINEERING | 2011年 / 8卷 / 04期

基金：

爱尔兰科学基金会;

关键词：

Infectious disease; endemic equilibrium state; global stability; mass action; direct Lyapunov method; Lyapunov function; compartment model; HIV; SEIR EPIDEMIOLOGIC MODEL; LYAPUNOV FUNCTIONS; VARYING INFECTIVITY; NONLINEAR INCIDENCE; STABILITY; DYNAMICS; REPRODUCTION; AIDS; SYSTEMS; TIME;

D O I：

10.3934/mbe.2011.8.1019

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 of compartment staged-progression models for infectious diseases with long infectious period, where there are multiple alternative disease progression pathways and branching. For example, these models reflect cases when there is considerable difference in virulence, or when only a part of the infected individuals undergoes a treatment whereas the rest remains untreated. Using the direct Lyapunov method, we establish sufficient and necessary conditions for the existence and global stability of a unique endemic equilibrium state, and for the stability of an infection-free equilibrium state.

引用

页码：1019 / 1034

页数：16

共 40 条

[1] ANDERSON R M, 1986, IMA Journal of Mathematics Applied in Medicine and Biology, V3, P229
[2] ANDERSON R M, 1991
[3] [Anonymous], 1988, MATH ECOLOGY
[4] [Anonymous], GLOBAL DYNAMIC PROPE
[5] Barbashin E.A., 1970, Introduction to the Theory of Stability
[6] ON THE GENERAL STRUCTURE OF EPIDEMIC SYSTEMS - GLOBAL ASYMPTOTIC STABILITY
BERETTA, E
CAPASSO, V
[J]. COMPUTERS & MATHEMATICS WITH APPLICATIONS-PART A, 1986, 12 (06): : 677 - 694
[7] DIEKMANN O, 1990, J MATH BIOL, V28, P365
[8] Endemic models with arbitrarily distributed periods of infection I: Fundamental properties of the model
Feng, ZL
Thieme, HR
[J]. SIAM JOURNAL ON APPLIED MATHEMATICS, 2000, 61 (03) : 803 - 833
[9] Global stability for a virus dynamics model with nonlinear incidence of infection and removal
Georgescu, Paul
Hsieh, Ying-Hen
[J]. SIAM JOURNAL ON APPLIED MATHEMATICS, 2006, 67 (02) : 337 - 353
[10] Goh B., 2012, Management and analysis of biological populations

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