Leaky or polarised immunity: non-Markovian modelling highlights the impact of immune memory assumptions

The biology of vaccine or infection-derived immunity effectiveness is sometimes overlooked by mathematical models. In particular, differences may arise when one chooses a polarised immunity – individuals are either fully susceptible or completely immune – compared to the leaky paradigm – where all individuals are partially protected up to a degree. We explore the differences between the two thanks to a non- Markovian formalism, which allows us to explicitly record the ‘age’ of the immunity and vary its effectiveness accordingly. A simple scenario reveals that leaky immunity leads to a shorter time between reinfections. A more realistic scenario based on SARS-CoV-2 data finds that leaky immunity yields substantially more reinfections than polarised immunity, along with a lower probability of hospitalisation and a higher number of infected individuals. Our results stress the importance of immune memory modelling assumptions, especially for long-term epidemiological dynamics and public health policies.