A spatial model of range-dependent succession

We consider an interacting particle system in which each site of the d-dime nsional integer lattice can be in state 0, 1, or 2. Our aim is to model the spread of disease in plant populations, so think of 0 = vacant, 1 = health y plant, 2 = infected plant. A vacant site becomes occupied by a plant at a rate which increases linearly with the number of plants within range R, up to some saturation level, F-1, above which the rate is constant. Similarly , a plant becomes infected at a rate which increases linearly with the numb er of infected plants within range M, up to some saturation level, F-2. An infected plant dies (and the site becomes vacant) at constant rate delta. W e discuss coexistence results in one and two dimensions. These results depe nd on the relative dispersal ranges for plants and disease.