Under the implementation of non-pharmaceutical interventions such as social distancing and lockdowns, household transmission has been shown to be significant for COVID-19, posing challenges for reducing incidence in settings where people are asked to self-isolate at home and to spend increasing amounts of time at home due to distancing measures. Accordingly, characteristics of households in a region have been shown to relate to transmission heterogeneity of the virus. We introduce a stochastic epidemiological model to examine the impact of the household size distribution in a region on the transmission dynamics. We choose parameters to reflect incidence in two health regions of the Greater Vancouver area in British Columbia and simulate the impact of distancing measures on transmission, with household size distribution the only different parameter between simulations for the two regions. Our result suggests that the dissimilarity in household size distribution alone can cause significant differences in incidence of the two regions, and the distributions drive distinct dynamics that match reported cases. Furthermore, our model suggests that offering individuals a place to isolate outside their household can speed the decline in cases, and does so more effectively where there are more larger households.