For this scenario, we have a perfectly homogeneous world except for an infective point source in the top left hand corner. Here each cell can only hold one host so some of the parameters become meaningless. For example, mmigration cannot occur unless there are deaths to create empty spaces and intra-cell or contact infection is obsolete because each host is alone it its cell. As the population becomes immune you can increase the resusceptibility probability to reset that immunity and increase the spontaneous infections to start a new outbreak.