Simplified model schema. On each day, unvaccinated people become vaccinated, with under-ascertainment ratio and . The probability that a newly vaccinated person has been infected before is proportional to the respective size of the subpopulation of recovered people that are eligible for vaccination Y. Furthermore, on each day, unvaccinated people become infected, with under-ascertainment ratio . The probability that a newly infected person has been infected before is proportional to the respective size of the subpopulation of recovered people that are eligible for reinfection (1 − r)Y, where 1 − r is the relative reinfection probability or ‘recovered immunity’. Recovered individuals are expected to reach eligibility for reinfection/vaccination after an average duration of τ. (Note that in the full model, breakthrough and reinfections of vaccinated individuals are possible (see SM, Sec. ‘Introduction’)).