A MATHEMATICAL DELAY MODEL FOR CONTROL OF THE SPREAD OF HIV/AIDS IN A HOMOGENEOUS POPULATION

Summary A non linear delay system of DDEs describing the dynamics of HIV inclusive of PEP was developed and the basic reproduction number was computed. Existence of steady Points were evaluated and analysis of the steady points was done and the following results were obtained. The uninfected steady point was proved to be local asymptotically stable provided $R_{\tau}<1$ for all $\tau>1$ while the Infected steady point was locally asymptotically stable when $R_{0}>1$ It was also found that the Uninfected Steady point was globally asymptotically stable provided $R_{\tau}<1$. On perfuming numerical simulations the disease was found to be Persistent when $\phi$ was zero and $\tau= 3$ days while when $\phi$ was $1$ and $\tau=0$ days the disease was controlled in the population.