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 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

L'equació de les plantes invasores

Els fenòmens naturals poden ser analitzats amb models teòrics, molts dels quals es poden plasmar amb unes equacions matemàtiques més o menys sofisticades. Aquest és el repte que ha afrontat un equip de físics teòrics amb les plantes invasores: elaborar un model matemàtic que permeti descriure i predir la capacitat d'invasió d'una planta en un ecosistema estrany i la velocitat d'ocupació dels nous territoris. El model contempla el cicle de vida de la planta, el seu ritme de creixement, la maduració de les seves llavors... Els resultats han estat confirmats per a vàries plantes invasores en diferents ecosistemes.Los fenómenos naturales pueden ser analizados con modelos teóricos, muchos de los cuales se pueden plasmar con unas ecuaciones matemáticas más o menos sofisticadas. Este es el reto que ha afrontado un equipo de físicos teóricos con las plantas invasoras: elaborar un modelo matemático que permita describir y predecir la capacidad de invasión de una planta en un ecosistema extraño y la velocidad de ocupación de los nuevos territorios. El modelo contempla el ciclo de vida de la planta, su ritmo de crecimiento, la maduración de sus semillas... Los resultados han sido confirmados para varias plantas invasoras en diferentes ecosistemas

First-passage times in multi-scale random walks: the impact of movement scales on search efficiency

An efficient searcher needs to balance properly the tradeoff between the exploration of new spatial areas and the exploitation of nearby resources, an idea which is at the core of scale-free L\'evy search strategies. Here we study multi-scale random walks as an approximation to the scale- free case and derive the exact expressions for their mean-first passage times in a one-dimensional finite domain. This allows us to provide a complete analytical description of the dynamics driving the asymmetric regime, in which both nearby and faraway targets are available to the searcher. For this regime, we prove that the combination of only two movement scales can be enough to outperform both balistic and L\'evy strategies. This two-scale strategy involves an optimal discrimination between the nearby and faraway targets, which is only possible by adjusting the range of values of the two movement scales to the typical distances between encounters. So, this optimization necessarily requires some prior information (albeit crude) about targets distances or distributions. Furthermore, we found that the incorporation of additional (three, four, ...) movement scales and its adjustment to target distances does not improve further the search efficiency. This allows us to claim that optimal random search strategies in the asymmetric regime actually arise through the informed combination of only two walk scales (related to the exploitative and the explorative scale, respectively), expanding on the well-known result that optimal strategies in strictly uninformed scenarios are achieved through L\'evy paths (or, equivalently, through a hierarchical combination of multiple scales)