Predicting the cumulative medical load of COVID-19 outbreaks after the peak in daily fatalities

Gros, C.; Valenti, R.; Schneider, L.; Gutsche, B.; Markovic, D.

The distinct ways the COVID-19 pandemics has been unfolding in different countries and regions suggest that local societal and governmental structures play an essential role both for the baseline infection rate and the short-term and long-term reaction to the outbreak. Here we investigate how societies as a whole, and governments, in particular, modulate the dynamics of a novel epidemic using a generalisation of the SIR model, the controlled SIR model. We posit that containment measures correspond to feedback between the status of the outbreak (the daily or the cumulative number of cases and fatalities) and the reproduction factor. We present the exact phase space solution of the controlled SIR model and use it to quantify containment policies for a large number of countries in terms of short- and long-term control parameters. Furthermore, we identified for numerous countries a relationship between the number of fatalities within a fixed period before and after the peak in daily fatalities. As the number of fatalities corresponds to the number of hospitalised patients, the relationship can be used to predict the cumulative medical load, once the effectiveness of outbreak suppression policies is established with sufficient certainty.