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

Qualitative Analysis of Causal Cosmological Models

The Einstein's field equations of Friedmann-Robertson-Walker universes filled with a dissipative fluid described by both the {\em truncated} and {\em non-truncated} causal transport equations are analyzed using techniques from dynamical systems theory. The equations of state, as well as the phase space, are different from those used in the recent literature. In the de Sitter expansion both the hydrodynamic approximation and the non-thermalizing condition can be fulfilled simultaneously. For $\Lambda=0$ these expansions turn out to be stable provided a certain parameter of the fluid is lower than 1/2. The more general case $\Lambda>0$ is studied in detail as well.Comment: RevTeX file, 23 pages. Accepted for publication in J. Math. Phy