Predicting the cumulative medical load of COVID-19 outbreaks after the peak in daily fatalities
Authors: Gros Claudius , Valenti Roser , Schneider Lukas , Gutsche Benedikt , Marković Dimitrije 
Published: September 2020

The distinct ways the COVID-19 pandemics has been unfolding in different countries and regions suggest that local societal and governmental structures play an important role not only for the the baseline infection rate, but also for the short-term and long-term reaction to the outbreak. We propose to investigate the question of how societies as a whole, and governments in particular, modulate the dynamics of a novel epidemic using a generalization of the SIR model, the controlled SIR model. We posit that containment measures are equivalent to a feedback between the status of the outbreak and the reproduction factor. Short-term control of an outbreak, corresponds in this framework to the reaction of governments and individuals to daily cases and fatalities. The reaction to the cumulative number of cases or deaths, and not to daily numbers, is captured in contrast by long-term control. 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. We find increased contributions of long-term control for countries and regions in which the outbreak was suppressed substantially together with a strong correlation between the strength of societal and governmental policies and the time needed to contain COVID-19 outbreaks. Furthermore, for numerous countries and regions we identified a predictive relation between the number of fatalities within a fixed period before and after the peak daily fatality count which predicts the cumulative medical load of COVID-19 outbreaks that should be expected after the peak. These results suggest applicability of the proposed model not only for understanding the outbreak dynamics, but also for predicting future cases and fatalities once the effectiveness of outbreak suppression policies is established with sufficient certainty.

Author summary

The country specific dynamics of the COVID-19 pandemics has been suggests that local societal response and governmental structures are critical 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 the controlled SIR model, a generalisation of a standard compartmental model used for modelling the dynamics of infectious diseases. 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 model parameters corresponding to long- and short-term control. 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.