Analytical investigation of compartmental models and measure for reactions of governments.

The ongoing coronavirus disease 2019 (COVID-19) pandemic poses a major threat to the worldwide health care. In this context, epidemic modelling is an integral part of containment strategies. Compartmental models are typically used for this purpose. Analytical solutions of the two distinct but connected Susceptible-Infectious-Recovered-Deceased (SIRD) and Susceptible-Infectious-Quarantine-Recovered (SIQR) models are presented in this study. Furthermore, the behaviour at the start of a disease outbreak is derived. This analysis shows that a combination of transmission, recovery and isolation rates dominates the behaviour at the start of an epidemic. In addition, the loss occurring due to quarantine and lockdown measures is investigated, where it can be observed that quarantine procedures lead to a smaller loss in comparison with lockdown regulations. Within this framework, optimized strategies that lead to a constant epidemic peak or a minimized loss are presented.