Dynamical behavior of HIV-1 epidemic model with time dependent delay

Abstract

The delayed HIV-1 infection mathematical model with two delays is proposed. One of which represents the latent period between the time of contacting and entering of virions into the target cells while the second one stands for virus production period between the new virions to be produced within and released from the infected cells. The basic reproduction number R0is found for the proposed model and it is proved that the uninfected steady state is globally asymptotically stable if R0< 1 and unstable if R0> 1. And if R0> 1, then an infected steady state occurs which is proved to be locally as well as globally asymptotically stable. The formulae for R0shows that it is the decreasing function of both delays.