%0 Book Section %1 statphys23_0677 %A Tome, T. %B Abstract Book of the XXIII IUPAP International Conference on Statistical Physics %C Genova, Italy %D 2007 %E Pietronero, Luciano %E Loreto, Vittorio %E Zapperi, Stefano %K automata cellular dynamics epidemic models predator-prey spatial spreading statphys23 sthocastic topic-10 %T Probabilistic cellular automata describing population biology problems %U http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=677 %X We consider probabilistic cellular automata to describe two population dynamic processes where interacting individuals of different species or classes are spatially distributed 1. The individuals are discrete and localized over the sites of a lattice. The interactions between them are local and described by sthocastic rules similar to the ones of the contact process . We set up pair mean-field approximations for the cellular automata and perform numerical simulations. We consider first the dynamics of a predator-prey system in which each site of a lattice can be occupied by individuals of each specie and the local predator-prey interactions are based on the processes of the Lotka-Volterra model. From the pair approximation we derive a quasi-spatial model which is able display stable self-sustained oscillations of the populational densities. The other population dynamic problem that we consider is the spreading of an epidemic in a community. In that case, the interacting individuals belong in different classes, susceptible (S), infective (I) and removed (R) and our probabilistic cellular automaton is defined by a set of local rules which incorporates the processes of the most simple SIR model. With the pair approximation for the cellular automaton we introduce a SIR model which takes into account spatial correlations. With this model we deduce the epidemic threshold and epidemic curves. 1) E. Arashiro and T. Tome, J. Phys. A 40, 887(2007).

@incollection{statphys23_0677, abstract = {We consider probabilistic cellular automata to describe two population dynamic processes where interacting individuals of different species or classes are spatially distributed [1]. The individuals are discrete and localized over the sites of a lattice. The interactions between them are local and described by sthocastic rules similar to the ones of the contact process . We set up pair mean-field approximations for the cellular automata and perform numerical simulations. We consider first the dynamics of a predator-prey system in which each site of a lattice can be occupied by individuals of each specie and the local predator-prey interactions are based on the processes of the Lotka-Volterra model. From the pair approximation we derive a quasi-spatial model which is able display stable self-sustained oscillations of the populational densities. The other population dynamic problem that we consider is the spreading of an epidemic in a community. In that case, the interacting individuals belong in different classes, susceptible (S), infective (I) and removed (R) and our probabilistic cellular automaton is defined by a set of local rules which incorporates the processes of the most simple SIR model. With the pair approximation for the cellular automaton we introduce a SIR model which takes into account spatial correlations. With this model we deduce the epidemic threshold and epidemic curves. 1) E. Arashiro and T. Tome, J. Phys. A 40, 887(2007).}, added-at = {2007-06-20T10:16:09.000+0200}, address = {Genova, Italy}, author = {Tome, T.}, biburl = {https://www.bibsonomy.org/bibtex/208108b7d956a25d394d1559e5ef9078e/statphys23}, booktitle = {Abstract Book of the XXIII IUPAP International Conference on Statistical Physics}, editor = {Pietronero, Luciano and Loreto, Vittorio and Zapperi, Stefano}, interhash = {bf74a912131f9570fb93c84c2c2fa954}, intrahash = {08108b7d956a25d394d1559e5ef9078e}, keywords = {automata cellular dynamics epidemic models predator-prey spatial spreading statphys23 sthocastic topic-10}, month = {9-13 July}, timestamp = {2007-06-20T10:16:26.000+0200}, title = {Probabilistic cellular automata describing population biology problems}, url = {http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=677}, year = 2007 }