The COVID-19 Outbreak In Germany – Models And Parameter Estimation

Since the end of 2019 an outbreak of a new strain of coronavirus, called SARS-CoV-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 Robert Koch 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 SEIRD 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 Monte Carlo based Metropolis algorithm.

An epidemic model integrating direct and fomite transmission as well as household structure applied to COVID-19.

This paper stresses its base contribution on a new SIR-type model including direct and fomite transmission as well as the effect of distinct household structures. The model derivation is modulated by several mechanistic processes inherent from typical airborne diseases. The notion of minimum contact radius is included in the direct transmission, facilitating the arguments on physical distancing. As fomite transmission heavily relates to former-trace of sneezes, the vector field of the system naturally contains an integral kernel with time delay indicating the contribution of undetected and non-quarantined asymptomatic cases in accumulating the historical contamination of surfaces. We then increase the complexity by including the different transmission routines within and between households. For airborne diseases, within-household interactions play a significant role in the propagation of the disease rendering countrywide effect. Two steps were taken to include the effect of household structure. The first step subdivides the entire compartments (susceptible, exposed, asymptomatic, symptomatic, recovered, death) into the household level and different infection rates for the direct transmission within and between households were distinguished. Under predefined conditions and assumptions, the governing system on household level can be raised to the community level. The second step then raises the governing system to the country level, where the final state variables estimate the total individuals from all compartments in the country. Two key attributes related to the household structure (number of local households and number of household members) effectively classify countries to be of low or high risk in terms of effective disease propagation. The basic reproductive number is calculated and its biological meaning is invoked properly. The numerical methods for solving the DIDE-system and the parameter estimation problem were mentioned. Our optimal model solutions are in quite good agreement with datasets of COVID-19 active cases and related deaths from Germany and Sri Lanka in early infection, allowing us to hypothesize several unobservable situations in the two countries. Focusing on extending minimum contact radius and reducing the intensity of individual activities, we were able to synthesize the key parameters telling what to practice.

Early stage COVID-19 disease dynamics in Germany: models and parameter identification.

Since the end of 2019 an outbreak of a new strain of coronavirus, called SARS-CoV-2, is reported from China and later other parts of the world. Since January 21, World Health Organization (WHO) reports daily data on confirmed cases and deaths from both China and other countries (www.who.int/emergencies/diseases/novel-coronavirus-2019/situation-reports). The Johns Hopkins University (github.com/CSSEGISandData/COVID-19/blob/master/csse_COVID_19_data/csse_COVID_19_time_series/time_series_COVID19_confirmed_global.csv) collects those data from various sources worldwide on a daily basis. For Germany, the Robert-Koch-Institute (RKI) also issues daily reports on the current number of infections and infection related fatal cases (www.rki.de/DE/Content/InfAZ/N/Neuartiges_Coronavirus/Situationsberichte/Gesamt.html). However, due to delays in the data collection, the data from RKI always lags behind those reported by Johns Hopkins. In this work we present an extended SEIRD-model to describe the disease dynamics in Germany. The parameter values are identified by matching the model output to the officially reported cases. An additional parameter to capture the influence of unidentified cases is also included in the model.