In this work, we quantify the rate at which non-pharmaceutical interventions can be lifted as COVID-19 vaccination campaigns progress. With the constraint of not exceeding ICU capacity, there exists only a relatively narrow range of plausible scenarios. We selected different scenarios ranging from the immediate release of restrictions to more conservative approaches aiming at low case numbers. In all considered scenarios, the increasing overall immunity (due to vaccination or post-infection) will allow for a steady increase in contacts. However, deaths and total cases (potentially leading to long covid) are only minimized when aiming for low case numbers, and restrictions are lifted at the pace of vaccination. These qualitative results are general. Taking EU countries as quantitative examples, we observe larger differences only in the long-term perspectives, mainly due to varying seroprevalence and vaccine uptake. Thus, the recommendation is to keep case numbers as low as possible to facilitate test-trace-and-isolate programs, reduce mortality and morbidity, and offer better preparedness against emerging variants, potentially escaping immune responses. Keeping moderate preventive measures in place (such as improved hygiene, use of face masks, and moderate contact reduction) is highly recommended will further facilitate control.

How will the coronavirus disease 2019 (COVID-19) pandemic develop in the coming months and years? Based on an expert survey, we examine key aspects that are likely to influence COVID-19 in Europe. The future challenges and developments will strongly depend on the progress of national and global vaccination programs, the emergence and spread of variants of concern, and public responses to nonpharmaceutical interventions (NPIs). In the short term, many people are still unvaccinated, VOCs continue to emerge and spread, and mobility and population mixing is expected to increase over the summer. Therefore, policies that lift restrictions too much and too early risk another damaging wave. This challenge remains despite the reduced opportunities for transmission due to vaccination progress and reduced indoor mixing in the summer. In autumn 2021, increased indoor activity might accelerate the spreadagain, but a necessary reintroduction of NPIs might be too slow. The incidence may strongly rise again, possibly filling intensive care units, if vaccination levels are not high enough. A moderate, adaptive level of NPIs will thus remain necessary. These epidemiological aspects are put into perspective with the economic, social, and health-related consequences and thereby provide a holistic perspective on the future of COVID-19.

As SARS-CoV-2 is becoming endemic, a sustainable strategy to manage the pandemic is needed, especially when facing a steep wave. We identified a metastable regime at low case numbers, where test-trace-and-isolate (TTI) together with moderate contact reduction is sufficient to control the spread.

However, this control is lost once case numbers overwhelm the limited TTI capacity. Beyond that tipping point, increasingly more infectious individuals remain undetected, generating a self-accelerating spread. To reestablish control, a lockdown (circuit breaker) has to strike a delicate balance between duration, stringency, and timeliness; otherwise, lockdowns are ineffective, or their effect is soon lost. However, once reestablishing control at low case numbers, no additional lockdowns are necessary. In the long-term, immunity and large-scale testing will further facilitate the control of COVID-19.

A second wave of SARS-CoV-2 is unfolding in dozens of countries. However, this second wave manifests itself strongly in new reported cases, but less in death counts compared to the first wave. Over the past three months in Germany, the reported cases increased by a factor five or more, whereas the death counts hardly grew. This discrepancy fueled speculations that the rise of reported cases would not reflect a second wave but only wider testing.

We find that this apparent discrepancy can be explained to a large extent by the age structure of the infected, and predict a pronounced increase of death counts in the near future, as the spread once again expands into older age groups. To re-establish control, and to avoid the tipping point when TTI capacity is exceeded, case numbers have to be lowered. Otherwise the control of the spread and the protection of vulnerable people will require more restrictive measures latest when the hospital capacity is reached.

Without a cure, vaccine, or proven long-term immunity against SARS-CoV-2, test-trace-and-isolate (TTI) strategies present a promising tool to contain the viral spread. For any TTI strategy, however, a major challenge arises from pre- and asymptomatic transmission as well as TTI-avoiders, which contribute to "hidden", unnoticed infection chains.

In our semi-analytical model, we identified two distinct tipping points between controlled and uncontrolled spreading: one, at which the behavior-driven reproduction number $R$_t^H of the hidden infections becomes too large to be compensated by the available TTI capabilities, and one at which the number of new infections starts to exceed the tracing capacity, causing a self-accelerating spread.

We investigated how these tipping points depend on realistic limitations like limited cooperativity, missing contacts, and imperfect isolation, finding that TTI is likely not sufficient to contain the natural spread of SARS-CoV-2. Therefore, complementary measures like reduced physical contacts and improved hygiene probably remain necessary.

In these technical notes, we provide detailed background information for our work on Bayesian inference of change-points in the spread of SARS-CoV-2 and the effectiveness of non-pharmaceutical interventions (Dehning et al., Science, 2020).

We outline the general background of Bayesian inference and of SIR-like models. We explain the assumptions that underlie model-based estimates of the reproduction number and compare them to the assumptions that underlie model-free estimates, such as used in the Robert-Koch Institute situation reports. We highlight effects that originate from the two estimation approaches, and how they may cause differences in the inferred reproduction number.

Furthermore, we explore the challenges that originate from data availability — such as publication delays and inconsistent testing — and explain their impact on the time-course of inferred case numbers. Along with alternative data sources, this allowed us to cross-check and verify our previous results.

The self-avoiding walk is one of the simples basic problems in statistical physics. Nonetheless, few properties can be determined in a rigorous mathematical fashion. In short a self-avoiding walk is a sequence of moves on a lattice also sometimes called a path. Theses paths are not allowed to cross over themself i.e. they do not visit a site more than once. One can use the framework of Monte Carlo methods to get good estimates for local and global properties of such paths.

In my bachelors thesis I looked at a further restricted type of self-avoiding walk, the periodic self-avoiding walk. These periodic self-avoiding walks have to additionally suffice periodic boundary conditions on a lattice. Overall there was a lot of work done for the normal self-avoiding walk but barely anything for the periodic case. Therefore, I choose the periodic self-avoiding walk as my topic for the bachelors thesis.

Specifically, I wrote a program for the enumeration of short periodic self-avoiding walks and another one for the Monte Carlo simulation of longer walks. I compared important properties such as end to end distance or gyration radius between the exact enumeration and the approximations from Monte Carlo simulation. All programs were written in C++ and the data was evaluated using python and matplotlib. If all of that sound interesting or fun to you, feel free to take a look.

The website shows a map of the weekly reported SARS-CoV-2 by age group and Region (Landkreis). The website and underling analysis was used as basis for multiple German press articles (e.g. ZDF, PNN or Focus). For the weekly cases I use a rolling sum of the last 7 days. The incidence (cases per 100.000 residents) is calculated using the population data retrieved from destatis. The website should update every 4 hours via a github workflow. It uses higcharts in the frontend for plotting and our python coronavirus toolbox for data retrieval.

This website was created to have an convenient way to change parameters in the numeric simulation of the differential equations in the "The challenges of containing SARS-CoV-2 via test-trace-and-isolate" publication (see above). The website was also used to validate the results i.e. mainly the plots of the paper which were generated with matlab beforehand. The numerical simulation is using Runge-Kutta 4 which I implemented using C++ and ported to the browser with WebAssembly. The interactive plots were created using HighCharts and the main layout was done via bootstrap. Overall this website was quite the fun project and taught me quite a lot about WebAssembly and interaction with binary code in the browser.

The website (the one you are viewing right now) was made with bootstrap v5 and native javascript. I took some visual inspiration from iPortfolio and if I copied some javascript code snippets from the web they are referenced in the source code.

Theses two websites were made for my mothers occupations to help her with freelancing work. They are actually my first two (public) websites, and I learned a lot from developing them. These websites were made using bootstrap v4, php and javascript. I haven't uploaded the source code yet but if you are interested in it feel free to contact me by any means.

The flocking algorithm was created by Craig Reynolds to simulate the as the name already tells "flocking" behaviour of birds. The algorithm was amongst others used to generate realistic behaving bat swarms in Tim Burton's Batman Returns (1992).

I used this algorithm to learn about OpenGL and 3D computer graphics in general. The small application was write in C++ using GLAD and GLFW. This created a I find very satisfying to watch animation. A short example can be seen on my github repository.

These applets were created for fun i.e. if I saw something interesting online and wanted to recreate it or in my early days as student to apply things I learned in the university. I haven't uploaded all applets yet, but am working on it. For now there is a fractal, double pendulum and circle packing.