Abstract
We cluster time into intervals for the sake of computability—in fact, we approximate waning patterns by piecewise constant functions. In the analyses encompassing hybrid immunity (interactions), 2 intervals per an immunity source were the maximum; if we wanted to include all possible interactions (with finer clustering) the model would have too many parameters to be estimated.
The interval split points have been chosen to capture the waning pattern as clearly as possible: because waning of the postinfection immunity is slower than that of the postvaccination one (a fact we do not hide), the split point for the former should have been set longer (we chose 6 months) than that for the latter (we chose 2 months). Moreover, aware of model limitations, we ran several auxiliary analyses with a finer time granularity, also discerning between individual vaccines, but without interactions [2, supplementary material 2, sections 11–14].