This approximation holds as long as d i is large or the turning angle is low. The derivative of this second-order polynomial has a maximum in R=2. Second, we assessed the epidemiological impact of the hotspot on groups that never visit it because they range at a distance larger than R from the hotspot. For both models, when P B is high enough to allow some between-neighbour transmission, the attack rate for these groups was found to be larger than expected under a model with no hotspot (R = 0) (Fig. 4) . Stochastic, local between-group transmission events allow the spread of the disease beyond the radius of attraction. Groups that never visit the hotspot are thus indirectly impacted by the hotspot.