An HIV/AIDS model with vertical transmission and time delay∗

Abstract. We propose an HIV/AIDS model with vertical transmission and the period of sexual maturity of infected newborns which is incorporated in the model as a time delay. We have divided the sexually mature population into three subclasses: the susceptibles, the infectives and the AIDS population. Susceptibles are assumed to become HIV infected via sexual contacts with infectives. Model is analyzed using stability theory of differential equations. Both the infection-free and the endemic equilibria are found and their stability is investigated. Using Lyapunov functional approach, the sufficient conditions for global stability of the endemic equilibrium are obtained. It is shown that as the maturity period of infected newborns decreases, number of infectious individuals increases which in turn increases the AIDS population. Numerical simulations are also carried out to investigate the influence of key parameters on the spread of the disease, to support the analytical conclusion and illustrate possible behavioral scenario of the model