The reinfection threshold

被引:65
作者
Gomes, MGM
White, LJ
Medley, GF
机构
[1] Inst Gulbenkian Ciencias, P-2781901 Oeiras, Portugal
[2] Univ Warwick, Dept Biol Sci, Ecol & Epidemiol Grp, Coventry CV4 7AL, W Midlands, England
关键词
epidemiological model; partial immunity; reinfection threshold;
D O I
10.1016/j.jtbi.2005.03.001
中图分类号
Q [生物科学];
学科分类号
07 ; 0710 ; 09 ;
摘要
Thresholds in transmission are responsible for critical changes in infectious disease epidemiology. The epidemic threshold indicates whether infection invades a totally susceptible population. The reinfection threshold indicates whether self-sustained transmission occurs in a population that has developed a degree of partial immunity to the pathogen (by previous infection or vaccination). In models that combine susceptible and partially immune individuals, the reinfection threshold is technically not a bifurcation of equilibria as correctly pointed out by Breban and Blower. However, we show that a branch of equilibria to a reinfection submodel bifurcates from the disease-free equilibrium as transmission crosses this threshold. Consequently, the full model indicates that levels of infection increase by two orders of magnitude and the effect of mass vaccination becomes negligible as transmission increases across the reinfection threshold. (c) 2005 Elsevier Ltd. All rights reserved.
引用
收藏
页码:111 / 113
页数:3
相关论文
共 6 条
[1]  
BLOWER SM, 1998, MATH MODELS MED HLTH
[2]  
BREBAN R, 2005, J THEOR BIOL
[3]   A model for tuberculosis with exogenous reinfection [J].
Feng, ZL ;
Castillo-Chavez, C ;
Capurro, AF .
THEORETICAL POPULATION BIOLOGY, 2000, 57 (03) :235-247
[4]   The reinfection threshold promotes variability in tuberculosis epidemiology and vaccine efficacy [J].
Gomes, MGM ;
Franco, AO ;
Gomes, MC ;
Medley, GF .
PROCEEDINGS OF THE ROYAL SOCIETY B-BIOLOGICAL SCIENCES, 2004, 271 (1539) :617-623
[5]   Infection, reinfection, and vaccination under suboptimal immune protection: epidemiological perspectives [J].
Gomes, MGM ;
White, LJ ;
Medley, GF .
JOURNAL OF THEORETICAL BIOLOGY, 2004, 228 (04) :539-549
[6]   Contribution to the mathematical theory of epidemics [J].
Kermack, WO ;
McKendrick, AG .
PROCEEDINGS OF THE ROYAL SOCIETY OF LONDON SERIES A-CONTAINING PAPERS OF A MATHEMATICAL AND PHYSICAL CHARACTER, 1927, 115 (772) :700-721