While it is yet to be definitively shown how CD8+ T cells play a role in cross-reactivity and pre-existing immunity to SARS-CoV-2, other coronavirus and influenza infections, we were able to propose and mathematically model different hypotheses of CD8+ T cell cross-reactivity and evaluate their relevance to the dynamics of immune responses to SARS-CoV-2 (or other pathogens), making use of quantitative methods. Here, CD8A is linked to influenza.