ON AN INTERACTING PARTICLE SYSTEM MODELING AN EPIDEMIC

We consider an interacting particle system on Z(d) to model an epidemi c. Each site of Z(d) can be in either one of three states: empty, heal thy or infected. Healthy and infected individuals give birth at differ ent rates to healthy individuals on empty sites. Healthy individuals g et infected by infected individuals. Infected and healthy individuals die at different rates. We prove that in dimension 1 and with nearest- neighbor interactions the epidemic may persist forever if and only if the rate at which infected individuals give birth to healthy individua ls is high enough. This is in sharp contrast with models analysed by A ndjel and Schinazi (1994) and Sate et al. (1994) where infected indivi duals do not give birth. We also show that some results in the latter reference can be obtained easily and rigorously using probabilistic co upling to the contact process.