In this talk, we 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. It is the first time for us to use simple deterministic models to study this phenomenon. We use an increasing, saturating infectivity function to show the existence of viral blips in a 4-dimensional HIV antioxidant-therapy model. We propose four conditions for the existence of viral blips in a deterministic in-host infection model, and then apply these conditions to derive the simplest (2- and 3-dimensional) infection model which produces viral blips, and use stability theory to determine the complete parameter range for the 3-dimensional model in which blips are possible. Further, we find that a 5-dimensional immunological model satisfies the conditions and exhibits recurrent infection even with constant infectivity. This is a joint work with Wenjing Zhang and Lindi Wahl.