One of the most significant unanswered questions about COVID-19 epidemiology relates to the role of children in transmission. We estimate the susceptibility and infectivity of children compared to that of adults. We used data on 613 households in the city of Bnei-Brak, Israel, in which all family members were tested using PCR for COVID-19. We developed a novel estimation method based on a discrete stochastic dynamic model of the spread of the epidemic within a household. The model describes the propagation of the disease between household members allowing for susceptibility and infectivity parameters to vary among two age groups. The parameter estimates are obtained by a maximum likelihood method, where the likelihood function is constructed based on the stochastic model via simulations.