Bistable Dynamics and Hopf Bifurcation in a Refined Model of Early Stage\n HIV Infection

Recent clinical studies have shown that HIV disease pathogenesis can depend\nstrongly on many factors at the time of transmission, including the strength of\nthe initial viral load and the local availability of CD4+ T-cells. In this\narticle, a new within-host model of HIV infection that incorporates the\nhomeostatic proliferation of T-cells is formulated and analyzed. Due to the\neffects of this biological process, the influence of initial conditions on the\nproliferation of HIV infection is further elucidated. The identifiability of\nparameters within the model is investigated and a local stability analysis,\nwhich displays additional complexity in comparison to previous models, is\nconducted. The current study extends previous theoretical and computational\nwork on the early stages of the disease and leads to interesting nonlinear\ndynamics, including a parameter region featuring bistability of infectious and\nviral clearance equilibria and the appearance of a Hopf bifurcation within\nbiologically relevant parameter regimes.\n