# Master thesis on the mathematical modeling of Covid-19

For more than a year, politicians, scientists and society have been dealing with the question of the right measures to contain the Corona pandemic. Mathematical models, which – not only since Covid-19 – aim at predicting the course of epidemics as precisely as possible, play an important role. In this context, the Chair of Applied Mathematics and Numerical Analysis at the University of Wuppertal is now making a contribution: Under the supervision of mathematician Prof. Dr. Matthias Ehrhardt and health economist Prof. Dr. med. Helmut Brunner from the Schumpeter School of Business and Economics, graduate Sarah Marie Treibert developed her own complex model in her master’s thesis to describe the dynamics of the SARS-CoV-2 coronavirus as realistically as possible.

A common method for modeling epidemics is to divide the population into groups called compartments: those potentially susceptible to the virus, those infected but not yet infectious, those infected with symptoms, and those recovered or deceased. Over time, individuals move from one group to another. How dynamic this transition is depends significantly on three variables: the average number of contacts an infectious person has per day, the probability of transmission at contact, and how many days on average an individual is infectious. Together they form the basic reproduction number R0, the value of which ultimately tells us how many people an infectious person infects on average if the entire population is susceptible to the virus. With the help of these quantities, the transitions between the groups can also be formulated as equations, which – integrated into the mathematical model and adapted to real data – can finally be calculated and thus represent an image of the virus spread.

The aim of the models is to be able to make statements about future cases of disease as precisely as possible and also to provide a basis on which the success of certain strategic decisions and measures can be assessed. For example, scientific publications deal with the question of how the introduction of contact bans, exit restrictions or the wearing of mouth-nose protection affects the spread of the virus. It is obvious for all calculations that the more closely the population groups defined for the model are based on reality, the better the simulation. This is where Sarah Marie Treibert’s master’s thesis comes in. Her goal was to develop a complex core model on the basis of which various scenarios could subsequently be modeled flexibly and with which she wanted to stay as close as possible to reality. She divided the population not only into the four groups mentioned above, but also into a total of 13 different compartments, including people in quarantine, intensive care patients and vaccinated people, which she finally worked out for use in the mathematical model.

She then modeled two more scenarios herself, taking into account numerous parameters, and fed her models with real data from Germany and Sweden – including from the Robert Koch-Institute, the statistics portal Statista, the Intensive Care Register of the German Interdisciplinary Association for Intensive Care and Emergency Medicine, and the Swedish Health Authority. The considered data extends to the end of March 2021.

“The calculations showed, for example, that an increase in the ‘quarantine rate,’ that is, the proportion of the population protected from infection by imposed quarantine or non-pharmaceutical measures per week, results in the highest point of the incidence curve being reached much later, and lower at that. In addition, this has been shown to have a long-term effect on the dynamics of the viral progression. In addition, calculations using data from the first and second wave periods showed that there was no significant difference in the timing of the extreme reached in winter 2021/22 between Germany and Sweden,” Sarah Marie Treibert summarizes some of her findings.

Sarah Marie Treibert’s work shows tremendous quality and meticulousness. She has completely implemented her own thinking in the modeling. This work is an extremely successful example of the importance of mathematical modeling in areas relevant to society, as well as applied mathematics in general, whose research we are ambitiously pursuing here at University of Wuppertal.

The complete master thesis, including the used MATLB codes, is available here: http://elpub.bib.uni-wuppertal.de/servlets/DocumentServlet?id=11551
(Click on “Dateien”.)

Best regards
Matthias Ehrhardt