Deterministic epidemic models with explicit household structure

For a wide range of airborne infectious diseases, transmission within the family or household is a key mechanism for the spread and persistence of infection. In general, household-based transmission is relatively strong but only involves a limited number of individuals in contact with each infectious person. In contrast, transmission outside the household can be characterised by many contacts but a lower probability of transmission. Here we develop a relatively simple dynamical model that captures these two transmission regimes. We compare the dynamics of such models for a range of household sizes, whilst constraining all models to have equal early growth rate so that all models fit to the same early incidence observations of an epidemic. Finally we consider the use of prophylactic vaccination, responsive vaccination, or antivirals to combat epidemic spread and focus on whether it is optimal to target controls at entire households or to treat individuals independently.