In times of Corona, everyone looks at the reproduction number. But this important value is fraught with uncertainty. Professor Ralf Mikut's team at the Karlsruhe Institute of Technology (KIT) is now presenting a method for estimating the reproduction number that avoids time delays and compensates for weekday-related fluctuations. The scientists use an acausal filter with a filter length of seven days, which uses not only past and present but also future values. Their estimation is based on the same weekday of the previous week - similar to load forecasts in the energy sector.

The coronavirus pandemic continues to affect our lives - new information and current figures are available every day. In addition to the number of new cases, the reproduction number R is considered an important indicator of infection. The reproductive number indicates the average number of persons infected by an infected person. If R is above 1, this indicates that the number of new infections per day is increasing, which attracts particular public attention. Reproduction numnbers are of great importance in dealing with the pandemic. However, its estimation using mathematical models is subject to certain uncertainties, partly because the reported case numbers are weekday-dependent and local outbreaks cause them to rise sharply. Researchers at the Institute for Automation and Applied Computer Science (IAI) of the KIT have now developed a method for estimating a time-dependent reproduction number R that avoids undesired time delays and compensates for weekly periodicities. In a KIT publication, the scientists present their method using the example of SARS-CoV-2 infections and COVID-19, using data published by the Robert Koch Institute (RKI).

The reproduction number is based on the quotient of the number of new infections in two consecutive periods. To compensate for diagnosis, transmission and reporting delays, the estimate uses a statistical procedure known as nowcasting. A mathematical filter is used to smooth the data, for example to compensate for fluctuations over the course of the week or distortions caused by local outbreaks. For their method, the researchers used periods of seven days and applied a so-called causal filter. While causal filters only use past and present values, acausal filters also use future values. The estimation of future case numbers is based on the same weekday of the previous week. If necessary, holidays can also be taken into account.

Estimates of the reproduction number R according to a model of the Robert Koch Institute and a new model of the KIT. (Figure: Ralf Mikut, KIT)

"Acausal filters avoid unwanted time delays as they occur with causal filters", explains Professor Ralf Mikut, who designed the method. "The approach of estimating future figures on the basis of the same day of the previous week has proven its worth in other areas with weekly periodicity - for example, in load forecasting in energy time series". The Karlsruhe scientists compared their method with the existing RKI approaches and found that it better balances weekly periodicities and reduces phases in which R only appears to be above 1. 

From the project, which is funded by the Helmholtz Information & Data Science School for Health (HIDSS4Health) and the Helmholtz Artificial Intelligence Coorporation Unit (Helmholtz AI), the scientists derived the general recommendations to consistently check the weekday dependence of all results when estimating the number of reproductions, use filters with a filter length of seven days for weekday-dependent case numbers, and use causal filters to at least partially compensate for time delays.

Original publikcation (Open Access):
Ralf Mikut, Tillmann Mühlpfordt, Markus Reischl, Veit Hagenmeyer: Schätzung einer zeitabhängigen Reproduktionszahl R für Daten mit einer wöchentlichen Periodizität am Beispiel von SARS-CoV-2-Infektionen und COVID-19. KIT, 2020. DOI: 10.5445/IR/1000119466

https://publikationen.bibliothek.kit.edu/1000119466 


Code and Data:    
https://github.com/timueh/COVID-19 

See original press release (in German)