Generalising this exact result to larger households involves some complications. Consider for example a household of size 3, where one individual is infected at time t * = 0. The probability that neither of the other two individuals is infected by the first individual at time t * is q 3 t Ã ð Þ~exp {r 3 Ð tÃ 0 w s ð Þds À Á directly analogous to the situation for households of size 2. However this is somewhat greater than the actual probability that they are not infected at all, since once one of these two is infected, they can also infect the other, and thus the probability that they each escape infection is somewhat less than Q 3 :q 3 ?