### 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 language | English (US) |
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Pages (from-to) | 283-302 |

Number of pages | 20 |

Journal | Differential Equations and Dynamical Systems |

Volume | 19 |

Issue number | 4 |

DOIs | |

State | Published - Oct 1 2011 |

Externally published | Yes |

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### Keywords

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

### ASJC Scopus subject areas

- Analysis
- Applied Mathematics

### Cite this

*Differential Equations and Dynamical Systems*,

*19*(4), 283-302. https://doi.org/10.1007/s12591-011-0090-6