Covid-19 related research projects


Optimal control of epidemics

Project Heads

Markus Kantner, Thomas Koprucki

Project Members

Cooperation Partner

Project Duration

March – June 2020

Located at

Weierstrass Institute for Applied Analysis and Stochastics (WIAS)


When effective medical treatment and vaccination are not available, non-pharmaceutical interventions such as social distancing, home quarantine and far-reaching shutdown of public life are the only available strategies to prevent the spread of epidemics. Based on an extended SEIR model and optimal control theory, we computed the optimal non-pharmaceutical intervention strategy for the case that a vaccine is never found and complete containment is impossible. In this case, the control must meet competing requirements: First, the minimization of disease-related deaths, and, second, the establishment of a sufficient degree of natural immunity at the end of the measures, in order to exclude a second wave. Moreover, the socio-economic costs of the intervention shall be kept at a minimum. Our numerically computed control strategy is a single-intervention scenario that goes beyond heuristically motivated interventions and simple “flattening of the curve.” Careful analysis of the computed control strategy reveals, however, that the obtained solution is in fact a tightrope walk close to the stability boundary of the system, where socio-economic costs and the risk of a new outbreak must be constantly balanced against one another.


Mathematical epidemiology, optimal control, non-pharmaceutical interventions, effective reproduction number, dynamical systems, COVID-19, SARS-CoV2

More Information

Publication (Open Access):
M. Kantner and T. Koprucki: Beyond just “flattening the curve”: Optimal control of epidemics with purely non-pharmaceutical interventions. J. Math. Industry 10, 23 (2020) [Special Issue on SARS-CoV-2 Pandemics]




Article (Interview) in Verbundjournal 114, pp. 28–30 (2020)
G. Wiemer: „Mit Mathematik die Krise verstehen“/ „Understanding the crisis with mathematics“

Project Type

Project Funding