Mathematical modelling and analysis of HIV/AIDS transmission with vertical and horizontal transmission incorporating treatment as control strategy

Abstract

We developed a deterministic mathematical model in this study to study the vertical and horizontal dynamics of HIV/AIDS with treatment as a critical control measure. The basic reproduction number RH0 was calculated, and the model analysis shows that the system has a forward (transcritical) bifurcation at RH0 = 1. This means that, if RH0 < 1, the disease-free equilibrium is locally
asymptotically stable and unstable if RH0 > 1; and that there is one disease endemic equilibrium when RH0 > 1, which is locally asymptotically stable when RH0 > 1. A multi-parameter sensitivity analysis was performed to identify the impacts of the various parameters on RH0 . The findings indicate that the parameters whose sensitivity indices are positive contribute to the transmission and burden of HIV/AIDS in the population, for example, the contact rates. On the other hand, those with negative sensitivity indices, especially the treatment rates σh and σA, decrease the spread of the disease and diminish the infection pressure. In addition, numerical simulations were conducted by changing the key parameters, such as the treatment rates σh and σA, the vertical transmission rate βh, and the contact rate ω1. Results from the simulation suggest that the higher the treatment rates, the lower the HIV/AIDS prevalence rates and cumulative numbers of new infections, respectively, and the higher the contact and vertical transmission rates, the more the spread of the disease is intensified. Overall, the results indicate that combining treatment with prevention is critical to the control of the dynamics of HIV/AIDS transmission.