As a result of the last assumption and of the discussion around equation (6), the infectiousness functions can be decomposed as b G (t) = R G w (t) and b n (n, t) = r n w (t), where R G is the average number of people each infected individual infects through random (non-household) contacts, w (t) is the generation time distribution for between household transmission, and r n is a parameter describing infection within the household whose interpretation will be clarified below.