Before revision:  We model cross-reactive cellular adaptive immune responses induced by multiple infections, and show how the formation and re-activation of memory T cells explains observed shortening of a second infection when cross-reactivity is present .
After revision:  We model cross-reactive cellular adaptive immune response: the initial naive T cell number, the avidity of the interaction between T cells and the epitopes presented by infected cells, and the epitope abundance per infected cell. Our model explains the experimentally observed shortening of a second infection when cross-reactivity is present .