BACKGROUND: Infection with severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) induces a complex antibody response that varies by orders of magnitude between individuals and over time. METHODS: We developed a multiplex serological test for measuring antibodies to five SARS-CoV-2 antigens and the Spike proteins of seasonal coronaviruses. We measured antibody responses in cohorts of hospitalized patients and healthcare workers followed for up to eleven months after symptoms. A mathematical model of antibody kinetics was used to quantify the duration of antibody responses. Antibody response data were used to train algorithms for estimating time since infection. RESULTS: One year after symptoms, we estimate that 36% (95% range: 11%, 94%) of anti-Spike IgG remains, 31% (9%, 89%) anti-RBD IgG remains, and 7% (1%, 31%) anti-Nucleocapsid IgG remains. The multiplex assay classified previous infections into time intervals of 0-3 months, 3-6 months, and 6-12 months. This method was validated using data from a sero-prevalence survey in France, demonstrating that historical SARS-CoV-2 transmission can be reconstructed using samples from a single survey. CONCLUSIONS: In addition to diagnosing previous SARS-CoV-2 infection, multiplex serological assays can estimate the time since infection which can be used to reconstruct past epidemics.