where 2L q 2 (t * )/Lt * is the rate of change of the cumulative probability of not being infected, i.e. the probability density of being infected at time t * , and the normalising factor 1-Q 2 is the total probability of being infected. The difference between w 2 (t * ) and the standard generation time distribution w (t) is a saturation effect, so that the second case tends to get infected earlier as the infectiousness of the index case (r 2 ) is increased. The infectiousness of the second individual towards other nonhousehold members of the population, conditional on his or her infection, and described as a function of the time t * since the infection of the household is thus the convolution of w 2 (t * ) and b G (t), so that the total infectiousness of the household is