Model for acute stage HIV infection, A

Abstract

This document lays out a new within-host model of acute stage HIV infection. The acute stage of HIV infection is characterized by a sudden spike of viral load, followed by either complete clearance of the disease or a low level but persistent chronic infection. Clinical data suggests that the initial concentration of healthy T-cells and virions is vital to the dynamics of this early stage, but this is not well modeled by the standard three component model. More nuanced models have had better success at representing the spread of HIV at all stages, but include many awkward biological components and are infeasible to fit to actual data. The model in this document incorporates the homeostatic nature of the immune system to provide a model for the acute stage of the disease which represents interesting nonlinear dynamics. Chief among these are bistable equilibria and a Hopf bifurcation within biologically relevant parameter regimes and dependent on initial conditions of infection. Local stability analysis of T-cell and virus populations to variation of parameters is also conducted, which leads to additional complexity in comparison to previous models.