Post-pandemic modeling of COVID-19: Waning immunity determines recurrence frequency

There are many factors in the current phase of the COVID-19 pandemic that signal the need for new modeling ideas. In fact, most traditional infectious disease models do not address adequately the waning immunity, in particular as new emerging variants have been able to break the immune shield acquired either by previous infection by a different strain of the virus, or by inoculation of vaccines not effective for the current variant. Furthermore, in a post-pandemic landscape in which reporting is no longer a default, it is impossible to have reliable quantitative data at the population level. Our contribution to COVID-19 post-pandemic modeling is a simple mathematical predictive model along the age-distributed population framework, that can take into account the waning immunity in a transparent and easily controllable manner. Numerical simulations show that under static conditions, the model produces periodic solutions that are qualitatively similar to the reported data, with the period determined by the immunity waning profile. Evidence from the mathematical model indicates that the immunity dynamics is the main factor in the recurrence of infection spikes, however, irregular perturbation of the transmission rate, due to either mutations of the pathogen or human behavior, may result in suppression of recurrent spikes, and irregular time intervals between consecutive peaks. The spike amplitudes are sensitive to the transmission rate and vaccination strategies, but also to the skewness of the profile describing the waning immunity, suggesting that these factors should be taken into consideration when making predictions about future outbreaks.