Mathematical modelling of the dynamics of HIV vertical transmission with drug resistance

A non-linear mathematical model is proposed to study the dynamics of HIV vertical transmission with drug resistance. The study assumes that treatment leads to the evolution of drug resistance. Positivity and boundedness of solutions were analysed quantitatively. The existence and stability of disease-free and endemic equilibrium points were also analysed. Through the determination of the steady states solutions, stability analysis and the next-generation operator techniques, reproduction numbers were determined. It was found that if the reproduction number is less than unity, the disease is eradicated and if greater than unity, the disease persists in the community. It was further found that treatment as an intervention strategy can help to contain the HIV/AIDS epidemic but can lead to evolution of drug resistance. It was recommended that preventative strategies that will reduce risks associated with vertical transmission in the infected HIV parents should be intensified in order to reduce the evolution of drug resistance.