MiS Preprint Repository

We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV ( that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint

Corona, Mathematical Epidemiology, Herd Immunity, and Data

Stephan Luckhaus


This paper is about data and models for the SARS-Corona-2 infection.
<br /The most important result: With two different statistical estimates it is shown that the antibody study conducted in Gangelt, Germany is underestimating the number of infected by a factor of less than 0.7. This is probably due to an underrepresentation of asymptomatic and paucisymptomatic among the PCR positives that are used to estimate the sensitivity of the antibody test. This is equally true for similar studies.

The second most important point which is actually known in mathematics: There is a hierarchy of models and justified simplifications. The classical SIR model is still a good description of the course of the epidemy, in which sense is explained. For the planning of containment strategies on the other hand, a version with several subpopulations in needed. The notion of herd immunity is replaced by the notion of stability region in the parameter space of the respective immunization levels. What this means for the stochastic process of the spread of the virus is explained.

The third point is an empirical observation from the data of Vo'. There were two infection waves with different prognosis for the outcome of the disease. That proves that the amount of the virus load the susceptibles are exposed to, is of paramount importance, not only in the case of health workers.


Related publications

2020 Repository Open Access
Stephan Luckhaus

Corona, mathematical epidemiology, herd immunity, and data