Mathematical Model on the optimal control of HIV/AIDS transmission dynamics, incorporating the uninfected class after an effective exposure to the disease

Abstract

In this work, we formulated a mathematical model on HIV/AIDS transmission dynamics that incorporates the post-contact control measure. The six important compartments of the model are: Susceptible, under-3-day Exposed, Exposed-Uninfected, Treatment, Pre-AIDS, and AIDS. The next-generation operator approach was used to obtain the effective reproduction number ( R e ) . From the stability analysis, it was established that the disease-free equilibrium point of the model is locally asymptotically stable when the reproduction number is less than one ( R e < 1 ) , and that it has a unique endemic equilibrium whenever this number exceeds unity. In the optimal control model, both Pre-contact Preventive and Anti-retroviral therapy (ART) control measures were incorporated. Pontryagin’s maximum principle was used to form an optimal system. Seven control strategies were considered. The most cost-effective control measure was identified to be ‘the optimal application of Pre-contact preventive control measures’. In double control strategies, ‘The combined use of Pre-contact Preventive and Anti-retroviral therapy’ was also found to be better and most cost-effective than the other double control strategies in controlling the virus. The population dynamics of different classes with respect to the application of each of these strategies were simulated with MATLAB to assess the impact of these control measures on the control of the virus.