Over three years since the first identified SARS-CoV-2 case was discovered, the role of adolescents and children in spreading the virus remains unclear. Specifically, estimating the relative susceptibility of a child with respect to an adult is still an open question. In our work, we generalize a well-known household model for modeling infectious diseases, to include missing tests. Due to missingness, the likelihood of the generalized model cannot be maximized directly. Thus, we propose an estimation methodology, using a novel EM algorithm, for estimating the MLE in the presence of missing data. We implement the proposed mechanism using R software. Using a simulation study, we illustrate the performance of the proposed estimation methodology compared with the estimation procedure in the complete case. Finally, using the proposed estimation methodology we analyzed a dataset containing SARS-CoV-2 testing results, collected from the city of Bnei Brak, Israel, during the beginning of the pandemic. Using this dataset, we show that adolescents are less susceptible than adults, and children are less susceptible than adolescents.