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

TL;DR

This paper introduces a refined HIV infection model that incorporates T-cell homeostasis, revealing complex dynamics such as bistability and Hopf bifurcation, which depend on initial conditions and biological parameters.

Contribution

It presents a new within-host HIV model with T-cell proliferation, analyzing its stability and nonlinear dynamics, including bistability and bifurcations, extending previous theoretical work.

Findings

Identification of parameter regions with bistability of infection and clearance

Discovery of Hopf bifurcation leading to oscillatory dynamics

Enhanced understanding of initial condition effects on disease progression

Abstract

Recent clinical studies have shown that HIV disease pathogenesis can depend strongly on many factors at the time of transmission, including the strength of the initial viral load and the local availability of CD4+ T-cells. In this article, a new within-host model of HIV infection that incorporates the homeostatic proliferation of T-cells is formulated and analyzed. Due to the effects of this biological process, the influence of initial conditions on the proliferation of HIV infection is further elucidated. The identifiability of parameters within the model is investigated and a local stability analysis, which displays additional complexity in comparison to previous models, is conducted. The current study extends previous theoretical and computational work on the early stages of the disease and leads to interesting nonlinear dynamics, including a parameter region featuring bistability of infectious and viral clearance equilibria and the appearance of a Hopf bifurcation within biologically relevant parameter regimes.