Serology tests for SARS-CoV-2 provide a paradigm for estimating the number of individuals who have had infection in the past (including cases that are not detected by routine testing, which has varied over the course of the pandemic and between jurisdictions). Classical statistical approaches to such estimation do not incorporate case counts over time, and may be inaccurate due to uncertainty about the sensitivity and specificity of the serology test. In this work, we provide a joint Bayesian model for case counts and serological data, integrating uncertainty through priors on the sensitivity and specificity. We also model the Phases of the pandemic with exponential growth and decay. This model improves upon maximum likelihood estimates by conditioning on more data, and by taking into account the epidemiological trajectory. We apply our model to the greater Vancouver area, British Columbia, Canada with data acquired during Phase 1 of the pandemic.Competing Interest StatementThe authors have declared no competing interest.Funding StatementThe work was funded by Genome B.C.textquoterights COVID-19 Rapid Response Funding Initiative (project code COV-142).