EpideMSE – Epidemiological Modeling, Simulation and Decision Support of COVID-19
When the Covid19-Pandemic started in early 2020, Germany reacted with strict, acute nationwide measures that aimed at minimizing infection risk within the population. These included closing possible meeting locations such as schools, non-essential shops, playgrounds, restaurants and the like. Now that the numbers have declined, the government was and is faced with the dilemma of balancing citizens’ freedom rights against the risk of a new wave of infection. With smaller, but heterogeneously distributed outbreaks, local health authorities and politicians are now responsible for deciding on the degree of relaxation of protective measures in their administrative districts. There are currently numerous publications and pre-publications (cf. Flaxman, 2020) in which scientists analyze the current infection situation and attempt to predict the further course of the pandemic. Nevertheless, it cannot be expected that a district administrator or the head of the local health department will have the time and training to apply the study results, which were prepared for specific countries, regions or cities, to the situation in his or her district.
At the Fraunhofer Institute for Industrial Mathematics ITWM in Kaiserslautern, Germany, employees from three different departments (“Transport Processes”, “Dynamics, Loads and Environmental Data” and “Optimization”) with their respective competences have joined forces in the Fraunhofer internal research project EpideMSE. Together they are developing a decision support tool that focuses on the regional decision level. On the one hand, data on historical and current infection incidents from various sources are continuously updated and bundled on a platform and supplemented by estimated dark figures. The core element, however, is the forecast of epidemiological key figures, especially under changed containment measures. This forecast model is now to be coupled with data from interaction matrices of different social sectors such that the effect of a measure only affects the interactions of certain population groups – e.g. doctors, teachers or schoolchildren. With this model, infection, hospitalization and death rates can be estimated.
Data Based Estimation of Dark Figures
The official information on the degree of spread of the novel corona virus in the population can only be as accurate as the tests performed allow. Thus, if testing is scaled back, the reported rates of new infections will decrease, but the number of people actually infected will – since undetected – increase even more. For effective containment of the infection rate, it is therefore essential to estimate the true number of infections and to include this information in the decision on measures to be taken. Since we cannot currently assume that sufficient (rapid) tests are available to systematically test the entire population frequently, we limit ourselves to a conservative, statistical estimate of the number of unreported cases based on freely available data. The core idea is firstly that some population groups are underrepresented in the official statistics because they are less prone to severe disease progression. However, according to their social interactions, infection is actually more likely. Also, data from other countries is being used to calibrate the data with respect to lethality rates which can be considered being dependent of age and sex, but independent of nationality. While the first implementations took a long time to calculate and estimate individual dark figures for all 402 German counties, we have been able to reduce the calculation effort significantly.
Estimation of Dark Figures (Screenshot/Graphics in German)
Epidemiological Models for Sars-Cov-2 Spread Prediction
Since we do not only want to look at the epidemic situation in its historical course, but above all to provide decision support for the near future, it is important that we can also forecast it. For this purpose we use a cohort based multi-group model with retardation. The groups are separated spatially and by age. Protection measures are modeled by changing contact rates as well as detection rates and times. The model is based on a classical SEIR approach, in which the populations are sorted into the categories Susceptible, Exposed, Infectious and Removed and their transitions are modeled using integro differential equations. Recently, the relation between standard SEIR models and our model with delay was investigated in depth. In particular, it turns out that a freely developing system saturates at lower numbers of infected persons, if our new model is used with the same initial conditions as a standard SEIR model. We model the dynamics of an epidemic by a differential system with delay. Usually, this requires initial values not only at the beginning of the simulation, but over a whole interval. However, analyzing the eigenvalues of the system, we could show that prescribing initial values at the start time is still enough as in standard SEIR models.
Regional Measures Analysis (Screenshot/Graphics in German)
At the end of German summer holidays we are again facing a dramatic increase of new infections, which cannot coherently explained within the model of a closed region. Therefore, we have added the possibility of external sources to our model in order to describe people who have been infected outside the simulated system, e.g. abroad.
Visualization and Decision Support
The (preliminary) models for estimation of unrecorded cases and dispersion models have already been combined in a web application, i.e. the forecast model can optionally take the hidden cases into account. To be able to make valid statements in the dynamic infection process, the local case numbers are updated daily. In order to test the effects of changing conditions, scenarios based on detection rates and reproduction figures can be calculated and visualized. We also visualize the data of the German Intensive Care Register and plan to incorporate their temporal development into the model fit.
Together with local decision-makers, the decision support system is applied to first pilot regions.
Intensive Care Bed Capacity (Screenshot/Graphics in German)
Author: Neele Leithäuser, Fraunhofer ITWM