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

摘要

This paper presents a deterministic model for evaluating the impact of anti-retroviral drugs (ARVs), voluntary testing (using standard antibody-based and a DNAbased testingmethods) and condom use on the transmission dynamics of HIV in a community. Rigorous qualitative analysis of themodel showthat 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.