The immune system has to decide on the reaction it will perform when it encounters a pathogen for the first time. The decision is based on the context in which the pathogen is presented and the signals it receives from the innate immune system. Thereafter responding naive lymphocytes will store the appropriate action by diverging to a specific phenotype. This allows to reproduce the same reaction upon a re-stimulation of the memory lymphocyte. If naive and memory lymphocytes recognize a pathogen, the naive lymphocytes will acquire the same phenotype as the memory lymphocytes. The effect of memory lymphocytes on naive ones can be deleterious if they cross react with pathogens which need a different type of immune reaction. Studies by Rob J. De Boer showed that the immune system has to be highly specific to avoid these mistakes but can still profit from the stored information. This project intends to have a closer look at the simulator Rob J. De Boer used in [1]. We will show that the simulator works well for the parameters used in [1] and that we have similar results if we change them. We will also present analytical formulas for some of the results of the simulation. This makes it easier to understand the shape of the graphs and the impact that the different lymphocytes have on each other, i.e. amount of deleted, auto immunity causing and memory lymphocytes of positive/negative reactions.