Household and community transmission parameters from final distributions of infections in households

A model is devised for the distribution of the total number of cases in households from a homogeneous community. In the model, community-acquired infection serves as a source of initial infection within households as well as of possible further cases. In addition, infected household members can infect others in the household. Maximum likelihood procedures for the model parameters are given. The model is fitted to symptom data on influenza and the common cold. Influenza seems to spread more easily in the community than within the household, while the opposite may be the case for the common cold. The model, which does not require specification of the time of onset of infection for individuals, can be fitted to serological data; this would provide a more accurate measure of household infection than the symptom data used.