Viral Blips May Not Need a Trigger: How Transient Viremia Can Arise in Deterministic In-Host Models

Abstract

Recurrent infection is characterized by short episodes of high viral reproduction, separated by long periods of relative quiescence. This recurrent pattern is observed in many persistent infections, including the “viral blips” observed during chronic infection with the human immunodeficiency virus (HIV). Although in-host models which incorporate forcing functions or stochastic elements have been shown to display viral blips, simple deterministic models also exhibit this phenomenon. We describe an analytical study of a 4-dimensional HIV antioxidant-therapy model which exhibits viral blips, showing that an increasing, saturating infectivity function contributes to the recurrent behavior of the model. Using dynamical systems theory, we hypothesize four conditions for the existence of viral blips in a deterministic in-host infection model. In particular, we explain how the blips are generated, which is not due to homoclinic bifurcation since no homoclinic orbits exist. These conditions allow us to develop very simple (2- and 3-dimensional) infection models which produce viral blips, and we determine the complete parameter range for the 3-dimensional model in which blips are possible, using stability analysis. We also use these conditions to demonstrate that low-dimensional in-host models with linear or constant infectivity functions cannot generate viral blips. Finally, we demonstrate that a 5-dimensional immunological model satisfies the conditions and exhibits recurrent infection even with constant infectivity; thus, an increasing, saturating infectivity function is not necessary if the model is sufficiently complex.