Vaccination strategies and backward bifurcation in an age-since-infection structured model

被引:78
作者
Kribs-Zaleta, CM
Martcheva, M
机构
[1] Polytech Univ, Dept Appl Math, Brooklyn, NY 11201 USA
[2] Univ Texas, Dept Math, Arlington, TX 76019 USA
关键词
backward bifurcation; variable infectivity; vaccination; SIRS model with chronic stage; age-since-infection structure;
D O I
10.1016/S0025-5564(01)00099-2
中图分类号
Q [生物科学];
学科分类号
07 ; 0710 ; 09 ;
摘要
We consider models for a disease with acute and chronic infective stages, and variable infectivity and recovery rates. within the context of a vaccination campaign. Models for SIRS and SIS disease cycles exhibit backward bifurcations under certain conditions, which complicate the criteria for success of the vaccination campaign by making it possible to have stable endemic states when R-0 < 1. We also show the extent to which the forms of the infectivity and recovery functions affect the possibility of backward bifurcations. SIR and SI models examined do not exhibit this behavior. (C) 2002 Elsevier Science Inc. All rights reserved.
引用
收藏
页码:317 / 332
页数:16
相关论文
共 20 条
[11]   A CORE GROUP MODEL FOR DISEASE TRANSMISSION [J].
HADELER, KP ;
CASTILLOCHAVEZ, C .
MATHEMATICAL BIOSCIENCES, 1995, 128 (1-2) :41-55
[12]   STABILITY AND BIFURCATION FOR A MULTIPLE-GROUP MODEL FOR THE DYNAMICS OF HIV AIDS TRANSMISSION [J].
HUANG, WZ ;
COOKE, KL ;
CASTILLOCHAVEZ, C .
SIAM JOURNAL ON APPLIED MATHEMATICS, 1992, 52 (03) :835-854
[13]   A MATHEMATICAL-MODEL OF EPIDEMICS WITH SCREENING AND VARIABLE INFECTIVITY [J].
KIM, MY ;
MILNER, FA .
MATHEMATICAL AND COMPUTER MODELLING, 1995, 21 (07) :29-42
[14]  
Kribs-Zaleta C, 2000, DYN CONTIN DISCRET I, V7, P1
[15]   A simple vaccination model with multiple endemic states [J].
Kribs-Zaleta, CM ;
Velasco-Hernández, JX .
MATHEMATICAL BIOSCIENCES, 2000, 164 (02) :183-201
[16]  
KRIBSZALETA CM, 2002, MODELS METHODS THEOR, V125, P269
[17]   A model of disease and vaccination for infections with acute and chronic phases [J].
Reade, B ;
Bowers, RG ;
Begon, M ;
Gaskell, R .
JOURNAL OF THEORETICAL BIOLOGY, 1998, 190 (04) :355-367
[18]   HOW MAY INFECTION-AGE-DEPENDENT INFECTIVITY AFFECT THE DYNAMICS OF HIV AIDS [J].
THIEME, HR ;
CASTILLOCHAVEZ, C .
SIAM JOURNAL ON APPLIED MATHEMATICS, 1993, 53 (05) :1447-1479
[19]   MINIMUM TRANSITION VALUES AND THE DYNAMICS OF SUBCRITICAL BIFURCATION [J].
TU, S ;
REISS, EL .
SIAM JOURNAL ON APPLIED MATHEMATICS, 1986, 46 (02) :189-198
[20]  
Wiggins S, 1990, INTRO APPL NONLINEAR, P194