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.
We present an agent-based model inspired by the Evolutionary Minority Game (EMG), albeit strongly adapted to the case of competition for limited resources in ecology. The agents in this game become able, after some time, to predict the a priori best
option as a result of an evolution-driven learning process. We show that a self-segregated social structure can emerge from this process, i.e., extreme learning strategies are always favoured while intermediate learning strategies tend to die out. This result may contribute to understanding some levels of organization and cooperative behaviour in ecological and social systems. We use the ideas and results reported here to discuss an issue of current interest in ecology: the mistimings in egg laying observed for some species of bird as a consequence of their slower rate of adaptation to climate change in comparison with that shown by their prey. Our model supports the hypothesis that habitat-specific constraints could explain why different populations are adapting differently to this situation, in agreement with recent experiments.
In this paper we reconsider the Mass Action Law (MAL) for the anomalous reversible reaction $Arightleftarrows B$ with diffusion. We provide a mesoscopic description of this reaction when the transitions between two states $A$ and $B$ are governed by
anomalous (heavy-tailed) waiting-time distributions. We derive the set of mesoscopic integro-differential equations for the mean densities of reacting and diffusing particles in both states. We show that the effective reaction rate memory kernels in these equations and the uniform asymptotic states depend on transport characteristics such as jumping rates. This is in contradiction with the classical picture of MAL. We find that transport can even induce an extinction of the particles such that the density of particles $A$ or $B$ tends asymptotically to zero. We verify analytical results by Monte Carlo simulations and show that the mesoscopic densities exhibit a transient growth before decay.
