Fraunhofer ITWM vs. Corona: Prediction Model for the Spread of Covid-19

Putting People into Pigeonholes Is Not an Option – Yes, It Is, for the Prediction of Covid-19 Spread!

Press Release / April 30, 2020

Researchers at the Fraunhofer Institute for Industrial Mathematics ITWM in Kaiserslautern are developing a prediction model for the spread of Covid-19 which, in contrast to classical models, is better able to detect "suddenly changing infection rates after actions have been taken". In addition, the researchers are simulating several spatially or age-separated groups in a network. The research work is being carried out as part of the "Fraunhofer vs. Corona" action program.

Putting people in pigeonholes or forming a three-class society - something that is by no means desired politically or socially - must sometimes be done when it comes to predicting the spread of infections. For a very long time, researchers have been working on the mathematical modelling of pandemics. The first publication on the subject dates from 1766, when Daniel Bernoulli, in his paper "Essai d'une nouvelle analyze de la mortalité causée par la petite vérole", developed a mathematical model to analyze the high mortality rate from smallpox in England. He was able to show that vaccinations increase life expectancy for newborns by an average of three years.

Especially when an infectious disease is new, mathematical models help to answer the two most important questions: How will the infection spread and what actions are appropriate and effective to controle it? What began in 1766 has developed over the past decades into a discipline in its own right, mathematical epidemiology. It includes not only the development of desease spread models based on differential equations, but also research into data-driven, statistical analyses of pandemics with spatial and temporal resolution. Machine learning is the latest discipline contributing to improved modelling and simulation of infection spread.

ITWM Improves WHO Model for the Simulation of Covid-19 Spread

The Fraunhofer ITWM is currently actively researching Covid-19 spread in Germany. For this purpose, the Mathematical Institute improved the existing classical models, which are discussed by the WHO for example (see website of the WHO).

Just as with the classic models, a population is divided into different clompartments. So far, the three-compartment model SIR and the four-compartment model SEIR have been used most frequently. In both models, "S" refers to the group of people who are susceptible to an infection, e.g. because they have not been vaccinated or have generally not yet developed antibodies against the infection. "I" describes the number of people who are infectious. With "R" we refer to the group that will be removed in the future. No distinction is made between people who recover and are immune in the future and those who die.

In the four-compartment model, the group of exposed "E" is added. This classifies persons who have already been infected with the virus but are not yet infectious themselves. Using differential equations, the transitions from one class to the next class are now calculated, thus simulating the number of infected people at any given time. The differential equations contain parameters such as the average duration of illness, which must be determined for each infectious disease from existing data and are disease-specific. This is in contrast to parameters that can be influenced politically, such as the basic reproduction rate. The basic reproduction rate indicates the average number of people infected by an infectious person and this parameter can be influenced by a society.

Time Delay Model for the Spread of Covid-19

In the classical models SIR and SEIR all model parameters are kept constant after they have been determined from the data. This is a serious drawback for the analysis of Covid-19 at this stage. Especially in order to analyze the effect of the lockdown actions and to be able to evaluate possible exit strategies, the model parameters must not be considered constant over time.

At the same time, an adequate model for the spread of Covid-19 must also take into account the fact that the effect of the actions occurs with a time delay. Therefore, the Fraunhofer ITWM has extended a classical SEIR model by time delay effects in order to be able to provide reliable spread predictions earlier than the classical models and thus enable the analysis of the actions. A further shortcoming of the classical models is that the dynamic of the epidemic is assumed to be homogenous across all regions and age groups. The Fraunhofer ITWM contrasts this assumption with cohorts, each with their own parameters and exchange coefficients. This also makes it possible to evaluate specialized actions, e.g. the opening of schools or relaxed contact restrictions in sparsely populated, rural regions.

Based on parameters adapted to publicly available case numbers, the ITWM research work around the scientists Dr. Jan Mohring and Dr. Raimund Wegener presents first predictions for the scenarios "herd immunity" and "eradication of the virus". In their results, they explain the two scenarios and use the basic reproduction rate to predict the duration and the chances of success of the scenarios.

Report on the Prediction Model for Download [Content in German] [ PDF 0.34 MB ]

© Fraunhofer ITWM
Scenario Herd Immunity

© Fraunhofer ITWM
Scenario Rapid Eradication of the Virus

Press Release

Fraunhofer ITWM vs. Corona: Prediction Model for the Spread of Covid-19

Putting People into Pigeonholes Is Not an Option – Yes, It Is, for the Prediction of Covid-19 Spread!

ITWM Improves WHO Model for the Simulation of Covid-19 Spread

Report on the Prediction Model

Further Information

Time Delay Model for the Spread of Covid-19

Contact Press / Media

Dr. Jan Mohring

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Dr. Raimund Wegener

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Prof.Dr. Simone Gramsch

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M.A. Esther Packullat