Conditions for transient viremia in deterministic in-host models: Viral blips need no exogenous trigger

Wenjing Zhang, Lindi M. Wahl, Pei Yu

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19 Scopus citations


This paper presents an analytical study of the phenomenon of recurrent infection, that is, transient episodes of high viral reproduction, separated by long periods of relative quiescence, which are observed in many persistent infections; the "viral blips" observed during chronic infection with human immunodeficiency virus (HIV) are a well-known example. Although in-host models which incorporate forcing functions or stochastic elements have been proposed to generate viral blips, simple deterministic models also exhibit this phenomenon. Analyzing a 4-dimensional HIV antioxidanttherapy model which exhibits viral blips, we show that an increasing, saturating infectivity function may contribute to the recurrent behavior of the model. We then propose four conditions for the existence of viral blips in a deterministic in-host infection model. We use these conditions to derive the simplest (2-and 3-dimensional) infection model which produces 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. Further, we find that a 5-dimensional immunological model satisfies the conditions and exhibits recurrent infection even with constant infectivity; thus, an increasing, saturating infectivity is not necessary if the model is sufficiently complex.

Original languageEnglish
Pages (from-to)853-881
Number of pages29
JournalSIAM Journal on Applied Mathematics
Issue number2
StatePublished - 2013


  • Bifurcation theory
  • Dynamical system
  • HIV viral blips
  • Recurrent infection


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