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

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.

Efficacy of Bacteriophage Treatment on Pseudomonas aeruginosa Biofilms

“…In addition, bacteria in older biofilms metabolize at a lower rate than those that are younger ones, especially if the bacteria are present in the deeper layers where the availability of oxygen and other nutrients is limited. As phage infection and phage life cycle are both dependent upon the growth stage of the host cell (119,151), it would be expected that the more slowly metabolizing cells present in older biofilms would demonstrate an increased degree of phage resistance (152). Since the reduction in biomass of the 96h biofilm in this study was comparable to that of the 24h biofilm after phage treatment, consideration had to be given as to why the expected outcome did not occur.…”

Genomic analyses of two novel biofilm-degrading methicillin-resistant Staphylococcus aureus phages

“…Furthermore, the bacterial metabolism in older biofilms continued to decrease at a lower rate, especially when the bacteria were present in the deeper layers of the biofilms where oxygen and nutrient availability are limited. As phage infection and phage life cycle are both dependent on the growth stage of the host cell [62], Azeredo and Sutherland [63] claimed that the more slowly-metabolizing cells present in the older biofilms would demonstrate an increased degree of phage resistance. Lenski [64] has claimed that in a closed system during phage-host interaction, the co-evolutionary potential of phage is less than their bacterial host strains, allowing bacterial mutants with no corresponding lytic phage strain to evolve.…”

Stabilization in a chemotaxis model for virus infection

“…Infected cells are produced at the rate βuw and die at rate d 2 v; 3. New virus is produced at a rate kv proportional to the number of infected cells, and die at a rate d 3 w. This model has been studied by several authors, for instance [5,7,17,24,25,27,38], who have studied the qualitative behavior of the solutions to the initial value problem enlightening a broad variety of asymptotic behaviors, related to the parameters of the model, which appear to be consistent with empirical data. An important role is acted by the so called basic reproduction number introduced by [21]…”

“…Various modifications have been proposed in the literature with the aim of going beyond the the simple description delivered by population dynamics without internal variables. Therefore, various technical modifications have been proposed, for instance, by introducing models with internal structure [7,37], stochastic interactions [11] and delay terms deemed to account also for the heterogeneity of individual entities of large biological systems [9], chapter 2. The books [9,28] refer this specific model to the existing literature in population dynamics, while the book by Nowak shows how evolutionary game theory can be used to model interactions and virus dynamics [23].…”