  We explore the role of cellular life cycles for viruses and host cells in an
infection process. For this purpose, we derive a generalized version of the
basic model of virus dynamics (Nowak, M.A., Bangham, C.R.M., 1996. Population
dynamics of immune responses to persistent viruses. Science 272, 74-79) from a
mesoscopic description. In its final form the model can be written as a set of
Volterra integrodifferential equations. We consider the role of age-distributed
delays for death times and the intracellular (eclipse) phase. These processes
are implemented by means of probability distribution functions. The basic
reproductive ratio $R_0$ of the infection is properly defined in terms of such
distributions by using an analysis of the equilibrium states and their
stability. It is concluded that the introduction of distributed delays can
strongly modify both the value of $R_0$ and the predictions for the virus
loads, so the effects on the infection dynamics are of major importance. We
also show how the model presented here can be applied to some simple situations
where direct comparison with experiments is possible. Specifically,
phage-bacteria interactions are analysed. The dynamics of the eclipse phase for
phages is characterized analytically, which allows us to compare the
performance of three different fittings proposed before for the one-step growth
curve.
