# The COVID-19 outbreak in Germany â€“ Models and Parameter Estimation

## Authors

• Peter Heidrich Mathematical Institute, University of Koblenzâ€“Landau, 56070 Koblenz
• Moritz SchÃ¤fer Mathematical Institute, University of Koblenzâ€“Landau, 56070 Koblenz
• Mostafa Nikouei Mathematical Institute, University of Koblenzâ€“Landau, 56070 Koblenz
• Thomas GÃ¶tz Mathematical Institute, University of Koblenzâ€“Landau, 56070 Koblenz

## Keywords:

COVIDâ€“19, Epidemiology, Disease dynamics, SEIRDâ€“model, Parameter estimation, Adjoint equations, Metropolis algorithm

## Abstract

Since the end of 2019 an outbreak of a new strain of coronavirus, called SARSâ€“CoVâ€“2, is reported from China and later also from other parts of the world. Since 21 January 2020, World Health Organization (WHO) reports daily data on confirmed cases and deaths from both China and other countries [1]. The Johns Hopkins University [2] collects those data from various sources worldwide on a daily basis. For Germany, the Robertâ€“Kochâ€“Institute (RKI) also issues daily reports on the current number of infections and infection related fatal cases and also provides estimates of several disease-related parameters [3]. In this work we present an extended SEIRDâ€“model to describe these disease dynamics in Germany. The model takes into account the susceptible, exposed, infected, recovered and deceased fractions of the population. Epidemiological parameters like the transmission rate, lethality or the detection rate of infected individuals are estimated by fitting the model output to available data. For the parameter estimation itself we compare two methods: an adjoint based approach and a Monteâ€“Carlo based Metropolis algorithm.

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