Subthreshold domain of bistable equilibria for a model of hiv epidemiology

B. D. Corbett, S. M. Moghadas, Abba Gumel

Research output: Contribution to journalArticle

10 Citations (Scopus)

Abstract

A homogeneous-mixing population model for HIV transmission, which incorporates an anti-HIV preventive vaccine, is studied qualitatively. The local and global stability analysis of the associated equilibria of the model reveals that the model can have multiple stable equilibria simultaneously. The epidemiological consequence of this (bistability) phenomenon is that the disease may still persist in the community even when the classical requirement of the basic reproductive number of infection (□O) being less than unity is satisfied. It is shown that under specific conditions, the community-wide eradication of HIV is feasible if □0<□□, where □□ is some threshold quantity less than unity. Furthermore, for the bistability case (which occurs when □□<□0<1), it is shown that HIV eradication is dependent on the initial sizes of the subpopulations of the model.

Original languageEnglish (US)
Pages (from-to)3679-3698
Number of pages20
JournalInternational Journal of Mathematics and Mathematical Sciences
Volume2003
Issue number58
DOIs
StatePublished - 2003
Externally publishedYes

Fingerprint

Epidemiology
Bistability
Basic Reproductive number
Global Analysis
Vaccine
Local Stability
Population Model
Global Stability
Infection
Stability Analysis
Model
Dependent
Requirements
Community

ASJC Scopus subject areas

  • Mathematics (miscellaneous)

Cite this

Subthreshold domain of bistable equilibria for a model of hiv epidemiology. / Corbett, B. D.; Moghadas, S. M.; Gumel, Abba.

In: International Journal of Mathematics and Mathematical Sciences, Vol. 2003, No. 58, 2003, p. 3679-3698.

Research output: Contribution to journalArticle

@article{da32acfc90e14d10b1d285efb250da0a,
title = "Subthreshold domain of bistable equilibria for a model of hiv epidemiology",
abstract = "A homogeneous-mixing population model for HIV transmission, which incorporates an anti-HIV preventive vaccine, is studied qualitatively. The local and global stability analysis of the associated equilibria of the model reveals that the model can have multiple stable equilibria simultaneously. The epidemiological consequence of this (bistability) phenomenon is that the disease may still persist in the community even when the classical requirement of the basic reproductive number of infection (□O) being less than unity is satisfied. It is shown that under specific conditions, the community-wide eradication of HIV is feasible if □0<□□, where □□ is some threshold quantity less than unity. Furthermore, for the bistability case (which occurs when □□<□0<1), it is shown that HIV eradication is dependent on the initial sizes of the subpopulations of the model.",
author = "Corbett, {B. D.} and Moghadas, {S. M.} and Abba Gumel",
year = "2003",
doi = "10.1155/S0161171203209224",
language = "English (US)",
volume = "2003",
pages = "3679--3698",
journal = "International Journal of Mathematics and Mathematical Sciences",
issn = "0161-1712",
publisher = "Hindawi Publishing Corporation",
number = "58",

}

TY - JOUR

T1 - Subthreshold domain of bistable equilibria for a model of hiv epidemiology

AU - Corbett, B. D.

AU - Moghadas, S. M.

AU - Gumel, Abba

PY - 2003

Y1 - 2003

N2 - A homogeneous-mixing population model for HIV transmission, which incorporates an anti-HIV preventive vaccine, is studied qualitatively. The local and global stability analysis of the associated equilibria of the model reveals that the model can have multiple stable equilibria simultaneously. The epidemiological consequence of this (bistability) phenomenon is that the disease may still persist in the community even when the classical requirement of the basic reproductive number of infection (□O) being less than unity is satisfied. It is shown that under specific conditions, the community-wide eradication of HIV is feasible if □0<□□, where □□ is some threshold quantity less than unity. Furthermore, for the bistability case (which occurs when □□<□0<1), it is shown that HIV eradication is dependent on the initial sizes of the subpopulations of the model.

AB - A homogeneous-mixing population model for HIV transmission, which incorporates an anti-HIV preventive vaccine, is studied qualitatively. The local and global stability analysis of the associated equilibria of the model reveals that the model can have multiple stable equilibria simultaneously. The epidemiological consequence of this (bistability) phenomenon is that the disease may still persist in the community even when the classical requirement of the basic reproductive number of infection (□O) being less than unity is satisfied. It is shown that under specific conditions, the community-wide eradication of HIV is feasible if □0<□□, where □□ is some threshold quantity less than unity. Furthermore, for the bistability case (which occurs when □□<□0<1), it is shown that HIV eradication is dependent on the initial sizes of the subpopulations of the model.

UR - http://www.scopus.com/inward/record.url?scp=17844381287&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=17844381287&partnerID=8YFLogxK

U2 - 10.1155/S0161171203209224

DO - 10.1155/S0161171203209224

M3 - Article

AN - SCOPUS:17844381287

VL - 2003

SP - 3679

EP - 3698

JO - International Journal of Mathematics and Mathematical Sciences

JF - International Journal of Mathematics and Mathematical Sciences

SN - 0161-1712

IS - 58

ER -