The effects of distributed life cycles on the dynamics of viral infections.
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 distributed lifespans and a 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 analyzed. 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.
Department of Applied Mathematics, School of Mathematics, The University of Manchester, Manchester M601QD, UK. Daniel.Campos@uab.es
Daniel
D
Campos
Vicenç
V
Méndez
Sergei
S
Fedotov
D000818:Animals; D001419:Bacteria / Q000821:virology; D001435:Bacteriophages / Q000502:physiology; D050936:Basic Reproduction Number; D002453:Cell Cycle / Q000502:physiology; D016923:Cell Death; D002477:Cells / Q000821:virology*; D008954:Models, Biological; D015233:Models, Statistical; D011336:Probability; D019562:Viral Load; D014777:Virus Diseases / Q000635:transmission*; D018406:Virus Physiological Phenomena