STABILITY ANALYSIS OF VERTICAL TRANSMISSION OF HIV WITH DELAYS IN TREATMENT AND PRE-AIDS

This paper proposes model of HIV transmission vertically with delays in treatment and pre-AIDS. In this model, the effect of sexually mature infected new borns as a time delay and effects of delay in treatment and pre-AIDS are analysed. Total population is divided into five compartments viz. Susceptible, Infectious, Treated, pre-AIDS and AIDS. The system of non-linear differential equations for the proposed problem is established. The next generation matrix method is used to find the reproduction number, and to obtain the stability of the infection free as well as the endemic equilibrium. Effect of time delays in Treatment, Infection and pre-AIDS has been studied for disease free equilibrium. The local and global stability of the system is analysed. Sensitivity of the key parameters is measured using numerical simulation and observed that it supports the analytical results.