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, A. B. Gumel, E. Strawbridge

Research output: Contribution to journalArticle

4 Scopus citations


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
Issue number4
StatePublished - Oct 1 2011
Externally publishedYes



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

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Cite this