The local transmission probability P i is defined as the per-timestep probability that a susceptible individual in group i is infected by an infectious individual from its own group or a neighbouring group. Let I i denote the number of infectious individuals in group i. The probability that the focal individual is infected by at least one of the infectious individuals in its own group is 1{ 1{P w ð Þ Ii , where P w is the within-group transmission probability from an infected individual to a susceptible individual of the same group. Likewise, the probability of a susceptible individual being infected by an infectious individual from one of the eight neighbouring groups is 1{ P