Local and global Hopf bifurcation analysis of an age-infection HIV dynamics model with cell-to-cell transmission

Abstract

In this study, we formulate an age-infection human immunodeficiency viruses (HIV) model incorporating cell-to-cell transmission and virus-to-cell infection. Our main goal is to investigate the local and global Hopf bifurcations of the model. We apply integrated semi-group, Hopf bifurcation theory and topological degree theorem. The theoretical analysis indicates that local and global bifurcation can occur from the positive steady state with respect to bifurcation parameters. These bifurcations are crucial for clinical treatment and experimental of HIV infections within the host. Because of the periodic oscillation, higher (or lower) virus load detected at a moment does not indicate the same high (or lower) load as time goes to infinity. At the same time, the appearance of periodic solution caused by time delay τ also explain the fluctuation of viral load in plasma. Finally, we presented some numerical simulations to validate our theoretical results.