Epidemiological dynamics in populations structured by neighbourhoods and households

Epidemiological dynamics are affected by the spatial and demographicstructure of the host population. Households and neighbourhoods are known to beimportant demographic structures but little is known about the epidemiologicalinterplay between them. Here we present a multi-scale model consisting ofneighbourhoods of households. In our analysis we focus on key parameters whichcontrol household size, the importance of transmission within householdsrelative to outside of them, and the degree to which the non-householdtransmission is localised within neighbourhoods. We construct the householdreproduction number $R_*$ over all neighbourhoods and derive the analyticprobability of an outbreak occurring from a single infected individual in aspecific neighbourhood. We find that reduced localisation of transmissionwithin neighbourhoods reduces $R_*$ when household size differs betweenneighbourhoods. This effect is amplified by larger differences betweenhousehold sizes and larger divergence between transmission rates withinhouseholds and outside of them. However, the impact of neighbourhoods withlarger household sizes is mainly limited to these neighbourhoods. We considervarious surveillance scenarios and show that household size information fromthe initial infectious cases is often more important than neighbourhoodinformation while household size and neighbourhood localisation influences thesequence of neighbourhoods in which an outbreak is observed.