. Consider now an individual in the i th generation of infection in the household, and consider this household at a time t * after the first index case was infected. This individual must have been infected at some earlier time s ( t * distributed according to the distribution w [i-1] (s). His or her infectiousness to others outside of the household will be given by b G (t * -s). Thus, by averaging over all possible values of s, the average infectiousness of such an individual in the i th generation is