Andronov-Hopf and Neimark-Sacker Bifurcations in Time-Delay Models of HIV Transmission

Rachadawan Darlai, Elvin J. Moore, Sanoe Koonprasert

Abstract

In this paper, we study the bifurcation properties of one-dimensional, time-delayed disease models for HIV.  The models include the effects of vertical HIV transmission from mother to baby,  the effects of births and deaths and of treatment by antivirals.  We first investigate the properties of  differential equation models and establish conditions for the existence  and stability of equilibrium points and for the existence of  Andronov-Hopf bifurcations at critical values of the time delays.  We then investigate the properties of discretized versions of the models and  establish conditions for the existence and stability of equilibrium points and  for the existence of Neimark-Sacker bifurcations at critical values of the time delays.