This thesis investigates the dynamics of T-cell populations during clonal expansion, utilizing mathematical models to replicate and analyze these processes. By focusing on single-cell resolution data from various cell families, the study aims to uncover heterogeneity in cell behavior. Comparisons among different approaches -Cyton, ODE and stochastic- highlight the Cyton model's superior adaptability in capturing complex dynamics. The work emphasises the need for nuanced models incorporating biological rules to better represent immune system responses.