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

Abstract

This paper presents a deterministic model for evaluating the impact of anti-retroviral drugs (ARVs), voluntary testing (using standard antibody-based and a DNAbased 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.

Mathematical dynamics for HIV infections with public awareness and viral load detectability

“…Theorem 6 The endemic equilibrium (EE), ϵ * * of model ( 1) is globally asymptotically stable (GAS) if R 0 > 1 and unstable if R 0 < 1.…”

“…The virus is transmitted via direct contact with different kinds of body fluids such as blood, vaginal fluids, rectal fluids, semen, and breast milk of the infected individual or through mother to her child during the pregnancy period (i.e, vertical transmission) [3,4]. HIV still remains one of the most severe global public health threats [5,6]. Since its emergence, more than 79.3 million people became infected with HIV/AIDS, among which 36.3 million people have died from AIDS-related illness [5].…”

“…The study by [10] showed that public health awareness on risk behaviours could help in decreasing the persistence of HIV/AIDS. A mathematical model for assessing the impact of condom usage, ART and voluntary testing in decreasing the spread of HIV was proposed by [6]. The study revealed that the hope of controlling HIV transmission using the intervention listed was highly remarkable.…”

“…The study recommended that to decrease the spread of HIV infections there is a need for personal precaution and periodic monitoring by researchers and medical professionals. For further references to the related studies mentioned above, one can visit [6,10,[17][18][19][20][21]. In this research work, we have formulated a new mathematical model of HIV/AIDS dynamics considering infected individuals with detectable viral load and infected individuals with undetectable viral load.…”