The effects of distributed life cycles on the dynamics of viral infections

TL;DR

This paper develops a generalized virus dynamics model incorporating distributed delays in cellular life cycles, revealing significant impacts on infection predictions and enabling comparison with experimental data, especially in phage-bacteria systems.

Contribution

It introduces a novel model with age-distributed delays for virus and host cell processes, extending previous models and analyzing their effects on infection dynamics.

Findings

Distributed delays significantly alter the basic reproductive ratio R0.

The model can be applied to experimental systems like phage-bacteria interactions.

Analytical characterization of the eclipse phase improves fitting of growth curves.

Abstract

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.