Mathematical Analysis of a Model for Assessing the Impact of Antiretroviral Therapy, Voluntary Testing and Condom Use in Curtailing the Spread of HIV

C. N. Podder, O. Sharomi, Abba Gumel, E. Strawbridge

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

This paper presents a deterministic model for evaluating the impact of anti-retroviral drugs (ARVs), voluntary testing (using standard antibody-based and a DNA-based testing methods) and condom use on the transmission dynamics of HIV in a community. Rigorous qualitative analysis of the model show that it has a globally-stable disease-free equilibrium whenever a certain epidemiological threshold, known as the effective reproduction number R eff, is less than unity. The model has an endemic equilibrium whenever R eff > 1. The endemic equilibrium is shown to be locally-asymptotically stable for a special case. Numerical simulations of the model show that the use of the combined testing and treatment strategy is more effective than the use of the standard ELISA testing method with ARV treatment, even for the use of condoms as a singular strategy. Furthermore, the universal strategy (which involves the use of condoms, the two testing methods and ARV treatment) is always more effective than the combined use of the standard ELISA testing method and ARVs.

Original languageEnglish (US)
Pages (from-to)283-302
Number of pages20
JournalDifferential Equations and Dynamical Systems
Volume19
Issue number4
DOIs
StatePublished - Oct 2011
Externally publishedYes

Fingerprint

Mathematical Analysis
Therapy
Testing
Enzyme-linked Immunosorbent Assay
Endemic Equilibrium
Model
Reproduction number
Deterministic Model
Qualitative Analysis
Asymptotically Stable
Antibody
Antibodies
Drugs
DNA
Numerical Simulation
Computer simulation
Strategy
Standards

Keywords

  • ARVs
  • Condoms
  • HIV
  • Nucleic acid amplification testing (NAAT)
  • Reproduction number
  • Stability
  • Standard testing

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Cite this

Mathematical Analysis of a Model for Assessing the Impact of Antiretroviral Therapy, Voluntary Testing and Condom Use in Curtailing the Spread of HIV. / Podder, C. N.; Sharomi, O.; Gumel, Abba; Strawbridge, E.

In: Differential Equations and Dynamical Systems, Vol. 19, No. 4, 10.2011, p. 283-302.

Research output: Contribution to journalArticle

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