9625126 Schinazi ABSTRACT Interacting particle systems are spatial stochastic models on a countable set (usually the lattice). The investigator uses these systems to model several biological phenomena. Many of these models have already been considered in the mathematical biology and physics literature but very few rigorous results have been proved. So far most of the mathematical theory about interacting particle systems deals with monotone (or attractive) systems. When one deals with epidemics, monotonicity does not hold. To prove results for non-monotone systems is crucial since so many phenomena in our world are not monotone in any (mathematically ) useful way. Interacting particle systems are very useful in studying epidemics. For instance, The investigator proposes the following model for the spread of an epidemic. There is a grid of sites and each site is either empty, healthy or infected. Healthy and infected individuals give birth to healthy individuals on empty nearest neighbor sites. Healthy individuals get infected by infected nearest neighbors. Healthy and infected individuals die at different rates. This seems adequate for epidemics like the AIDS epidemic for which infected individuals may give birth to healthy individuals. One of the results proved by The investigator is that, given an infection rate which is large enough, the epidemic will persist if and only if the rate at which infected individuals give birth is high enough. While the model considered is a gross simplification of the real world it does give an interesting idea to test. Namely, is it true that the countries where the AIDS epidemic is the most devastating are the countries where the rate at which infected individuals give birth is the highest?
