Individual traits, including comorbidities and age, define the immune response to viral infections and vaccines. Accounting for such traits is therefore critical to tailoring detection, treatment, and vaccination protocols. Mechanistic mathematical modelling helps to untangle the mechanisms contributing to differing outcomes, but the varying levels of heterogeneity that determine responses are frequently ignored. In this talk, I will describe how we use mechanistic mathematical modelling that accounts to individual-level heterogeneity to answer key questions about immune responses to viral infectious diseases and vaccination.