Overview: Why this Website?

Our motivation for this site is mainly to provide a little more insight into some of the standard mathematical and epidemiological methods used in modeling COVID-19, in a way that is accessible to a lay (but interested) audience. The methods described here are well known in the respective scientific communities.

We present an analysis of the COVID-19 pandemic in Austria using two standard approaches of mathematical epidemiology: an SEIR compartmental model and a method for so-called "R-Nowcasting" – estimating the effective reproduction number of the disease.

SEIR Model: Compartmental models, such as S-E-I-R, divide the population into groups based on disease status, typically Susceptible, Exposed, Infectious and Removed. (Individuals 'removed' from disease dynamics can neither spread nor contract the infection: for example, these are recovered individuals with life-long immunity.) The purpose of such a model is to understand how important parameters, such as the rate of transmission, affect the spread of the epidemic and ultimately influence how many people are infected. Our COVID-19 simulation tool gives the user an interactive way to experiment with different parameters to better understand their impact on the spread of the disease in Austria. Crucially, the objective is to achieve a qualitative understanding of the epidemic, not quantitative forecasting.

R-Nowcasting: The simulation app is complemented with a page devoted to “nowcasting”, a statistical analysis of available data that aims to understand what is happening to the epidemic right now. We calculate the value of the effective reproduction number R in Austria according to different statistical estimators, and provide some description of the mathematical background of the corresponding methods.

We would like to emphasize that the approaches we present here are limited in that they do not account for specific characteristics of COVID-19 that are only starting to emerge from ongoing scientific research, such as the phenomenon of superspreading. In particular, if the daily number of new infections is relatively low, such additional random effects play an important role and need to be considered to obtain a comprehensive picture of the evolution of COVID-19. However, this is beyond the scope of this site.

We would be happy to hear your feedback on how well we are succeeding at this goal, either through the feedback form, or by contacting us directly.


Dig deeper

There are many further approaches that are used to model the COVID-19 pandemic. We highlight some of the important work that others are doing in Austria. We may not be aware of all the groups that are working on COVID-19 related modeling in Austria. If your group is missing here and you would like to be added, do not hesitate to contact us.

An important class are so-called agent-based models, where people are not modeled as belonging to compartments, but represented individually as digital “person-agents” with their own geographic location and contact network in families, workplaces, schools, etc. This microscopic approach allows for great flexibility and the consideration of real-world details, if the parameters are known. Due to their complexity, these models typically take a lot of time to compute. A main model for the spread of COVID-19 in Austria is an agent-based model of this type, developed by the group of Niki Popper (TU Vienna and dwh GmbH).

In Austria the “Covid-Prognose-Konsortium” provides weekly short-time prognoses of the number of expected new infections. This is based on a combination and harmonization of three different modeling approaches consisting of an agent-based model, an SIRX-model, and a State-Space model. The “Covid-Prognose-Konsortium” consists of experts from TU Vienna / dwh GmbH, the Medical University of Vienna / Complexity Science Hub (CSH), and Gesundheit Österreich GmbH.

The group of Stefan Thurner / CSH has built a web-portal that provides a variety of national and international resources around COVID-19. Specifically, CSH has built an extensive database on the effectiveness of various containment strategies on an international level and has developed a traffic light system to monitor the spread of COVID-19 in different regions.

A leading role of the Austrian effort is played by AGES. In particular, AGES is the main source for the estimation of the reproductive number R in Austria and provides careful documentation of the relevant estimator. A further contribution that is of particular importance in the current stage of the epidemic concerns the analysis of new arising clusters.

The WPI (director: Norbert Mauser) has developed an analog model. The principial idea is that, based on an appropriate transformation, it is possible the leverage the early data from China to draw conclusions on the evolution of the epidemic in other countries.

Erich Neuwirth provides epidemiological data and statistical analyses / comparisons of the development of COVID-19 in Austria as well as many other countries that are updated on a daily basis. In addition he has developed a spread-sheet model that can easily be downloaded and modified to allow for hands-on experience with COVID-19-modeling.

Here are all these links in one big list:


Hauptuniversität IST ÖAW GMI