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Computational methods have been developped to simulate the complex interactions between components of the immune system. Chao introduced a method based on a stage structured approach to studying the Cytotoxic T cells response to an infection. In this work, we extend the analyzis of Chao’s simulater by Eric Winnington. We validate the time step choice used in the simulation and analyze the impact of different factors on the occurence of a secondary reaction. We find that the initialization of the simulation, and in particular the generation of the T Cell Receptor Chains and epitopes influences the frequency of this secondary reaction. Furthermore, we note that the secondary reaction arises in a time window when the number of na¨ıve cells population is low, the effector cell population is decreasing after the primary response and the memory T cells are not yet able to take part in the response. We find that the secondary reaction does not question the correctness of the simulation. The question of the adequacy of the biological model however remains open and is not discussed in this project.