We investigate the temporal evolution of the distribution of immunities in a population, which is determined by various
epidemiological, immunological, and demographical phenomena: after a disease outbreak, recovered individuals constitute a
large immune population; however, their immunity is waning in the long term and they may become susceptible again.
Meanwhile, their immunity can be boosted by repeated exposure to the pathogen, which is linked to the density of infected
individuals present in the population. This prolongs the length of their immunity. We consider a mathematical model
formulated as a coupled system of ordinary and partial differential equations that connects all these processes and systematically
compare a number of boosting assumptions proposed in the literature, showing that different boosting mechanisms lead to very
different stationary distributions of the immunity at the endemic steady state. In the situation of periodic disease outbreaks, the
waveforms of immunity distributions are studied and visualized. Our results show that there is a possibility to infer the boosting
mechanism from the population level immune dynamics.