Nearly two years into the pandemic, much remains unknown about the mechanisms leading to immunopathology in patients with COVID-19, including what controls the diversity of responses to SARS-CoV-2 infection. We have developed a mechanistic mathematical model of the immunological response to SARS-CoV-2 infection that includes several innate and adaptive immune cell populations and signalling pathways to answer fundamental questions about immunopathology and heterogeneity in COVID-19. By expanding a virtual patient cohort, we identified divergent monocyte-to-macrophage differentiation rates between virtual patients with either mild or severe COVID-19. Further, our results suggest that maximum IL-6 concentrations may act as a biomarker for CD8+ T cell depletion. Our approach provides a quantitative basis for exploring the drivers of immunopathology during SARS-CoV-2 infections, and a framework for the continued study of heterogeneity in COVID-19 and other during viral infections