At the molecular level, we observed that immune response to the influenza virus becomes diverse upon repeated viral exposures and can be presented as a fractal self-similar system. We proposed an adaptation of the Markov chain process to model the dynamics of memory T-cell repertoire considering typical experimental conditions. We derived model-inspired characteristics to quantify repertoires’ temporal stability and detected significant age-specific differences. These differences indicate that transitional probabilities are subject to change as the immune system evolves and could potentially serve as a marker of immunosenescence. We concluded that for infection with short immune memory, a boost via periodic vaccinations or direct exposures is critical for sustaining diverse immune responses.