Human societies have always lived with periodic epidemics and pandemics. Predicting how an outbreak may progress and spread is becoming essential to mitigate its effects, not only on population health and life expectancy, but also the societal upheaval and economic disruptions that come with it.

The field of epidemiology is therefore central, and since the beginning of the 20th century mathematical modeling techniques have increasingly played an important role in understanding the dynamics of the spread of diseases.

By extending the epidemiological SIR (Susceptible, Infectious, Recovered) model, the authors have developed an economic-epidemiological model with additional equations to represent quarantine measures where heterogeneous individuals are susceptible to being infected by a virus.

The resulting dynamic nonlinear optimization model is solved with Artelys Knitro. Thanks to its efficient interior-point method and its multi-start option, Artelys Knitro allows the authors to conduct an extensive analysis on the evolution of Covid-19 first wave in Germany.