by Bastien Reyné, Tsukushi Kamiya, Ramsès Djidjou-Demasse, Samuel Alizon, Mircea T. SofoneaMathematical models tend to oversimplify the biological details of vaccine or infection-derived immunity effectiveness. [0pc][-1pc]Please check and confirm the corresponding authors have been correctly identified amend if necessary.Yet, epidemiological outcomes may diverge when assuming polarised immunity—individuals are either fully susceptible or completely immune—compared to leaky immunity—where all individuals are partially protected. We explore the differences between the two by taking advantage of a non-Markovian framework, which allows us to explicitly record the ‘age’ of the immunity and vary its effectiveness accordingly. A basic scenario reveals that leaky immunity leads to a shorter time between reinfections. A more data-driven scenario based on SARS-CoV-2 data finds that leaky immunity yields substantially more reinfections than polarised immunity and a higher number of infected individuals, yet with a lower probability of hospitalisation. Our findings emphasize the critical role of immune memory modelling assumptions, especially for long-term epidemiological dynamics and public health policies.