Stability and bifurcation analysis of a class of delayed fractional differential equations describing the dynamics of HIV

In this paper, we propose a new delayed fractional-order model that describes the dynamics of human immunodeficiency virus (HIV). The proposed model incorporates three transmission modes, two types of infected cells, the adaptive immunity exerted by antibodies and CTL cells, two delays, one in viral production and the other in the activation time of antibodies, as well as four therapeutic parameters to represent different aspects of the therapy and the effect of memory described by Caputo fractional derivative. Additionally, we determine the equilibrium points and analyze their global stability with respect to specific threshold parameters. Moreover, we explore the existence of the Hopf bifurcation, demonstrating that the immune delay is the primary factor responsible for its occurrence.