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Grundel, Sara; Heyder, Stefan; Hotz, Thomas; Ritschel, Tobias K. S.; Sauerteig, Philipp; Worthmann, Karl;
How much testing and social distancing is required to control COVID-19? : some insight based on an age-differentiated compartmental model. - In: SIAM journal on control and optimization, ISSN 1095-7138, Bd. 60 (2022), 2, S. S145-S169

In this paper, we provide insights on how much testing and social distancing is required to control COVID-19. To this end, we develop a compartmental model that accounts for key aspects of the disease: incubation time, age-dependent symptom severity, and testing and hospitalization delays; the model's parameters are chosen based on medical evidence, and, for concreteness, adapted to the German situation. Then, optimal mass-testing and age-dependent social distancing policies are determined by solving optimal control problems both in open loop and within a model predictive control framework. We aim to minimize testing and/or social distancing until herd immunity sets in under a constraint on the number of available intensive care units. We find that an early and short lockdown is inevitable but can be slowly relaxed over the following months.
Bracher, Johannes; Wolffram, Daniel; Deuschel, Jannik; Görgen, Konstantin; Ketterer, Jakob L.; Ullrich, Alexander; Abbott, Sam; Barbarossa, Maria Vittoria; Bertsimas, Dimitris; Bhatia, Sangeeta; Bodych, Marcin; Bosse, Nikos I.; Burgard, Jan Pablo; Castro, Lauren; Fairchild, Geoffrey; Fuhrmann, Jan; Funk, Sebastian; Gogolewski, Krzysztof; Gu, Quanquan; Heyder, Stefan; Hotz, Thomas; Kheifetz, Yuri; Kirsten, Holger; Krueger, Tyll; Krymova, Ekaterina; Li, Michael Lingzhi; Meinke, Jan H.; Michaud, Isaac J.; Niedzielewski, Karol; Oża´nski, Tomasz; Rakowski, Franciszek; Scholz, Markus; Soni, Saksham; Srivastava, Ajitesh; Zieli´nski, Jakub; Zou, Difan; Gneiting, Tilmann; Schienle, Melanie;
A pre-registered short-term forecasting study of COVID-19 in Germany and Poland during the second wave. - In: Nature Communications, ISSN 2041-1723, Bd. 12 (2021), 5173, S. 1-16

Disease modelling has had considerable policy impact during the ongoing COVID-19 pandemic, and it is increasingly acknowledged that combining multiple models can improve the reliability of outputs. Here we report insights from ten weeks of collaborative short-term forecasting of COVID-19 in Germany and Poland (12 October-19 December 2020). The study period covers the onset of the second wave in both countries, with tightening non-pharmaceutical interventions (NPIs) and subsequently a decay (Poland) or plateau and renewed increase (Germany) in reported cases. Thirteen independent teams provided probabilistic real-time forecasts of COVID-19 cases and deaths. These were reported for lead times of one to four weeks, with evaluation focused on one- and two-week horizons, which are less affected by changing NPIs. Heterogeneity between forecasts was considerable both in terms of point predictions and forecast spread. Ensemble forecasts showed good relative performance, in particular in terms of coverage, but did not clearly dominate single-model predictions. The study was preregistered and will be followed up in future phases of the pandemic.
Grundel, Sara M.; Heyder, Stefan; Hotz, Thomas; Ritschel, Tobias K. S.; Sauerteig, Philipp; Worthmann, Karl;
How to coordinate vaccination and social distancing to mitigate SARS-CoV-2 outbreaks. - In: SIAM journal on applied dynamical systems, ISSN 1536-0040, Bd. 20 (2021), 2, S. 1135-1157

Most countries have started vaccinating people against COVID-19. However, due to limited production capacities and logistical challenges it will take months/years until herd immunity is achieved. Therefore, vaccination and social distancing have to be coordinated. In this paper, we provide some insight on this topic using optimization-based control on an age-differentiated compartmental model. For real-life decision-making, we investigate the impact of the planning horizon on the optimal vaccination/social distancing strategy. We find that in order to reduce social distancing in the long run, without overburdening the health care system, it is essential to vaccinate the people with the highest contact rates first. That is also the case if the objective is to minimize fatalities provided that the social distancing measures are sufficiently strict. However, for short-term planning it is optimal to focus on the high-risk group.
Chen, Liangzhi; Hotz, Thomas; Zhang, Haizhang;
Admissible kernels for RKHS embedding of probability distributions. - In: Statistical papers, ISSN 1613-9798, Bd. 62 (2021), 3, S. 1499-1518

Similarity measurement of two probability distributions is important in many applications of statistics. Embedding such distributions into a reproducing kernel Hilbert space (RKHS) has many favorable properties. The choice of the reproducing kernel is crucial in the approach. We study this question by considering the similarity of two distributions of the same class. In particular, we investigate when the RKHS embedding is "admissible" in the sense that the distance between the embeddings should become smaller when the expectations are getting closer or when the variance is increasing to infinity. We give conditions on the widely-used translation-invariant reproducing kernels to be admissible. We also extend the study to multivariate non-symmetric Gaussian distributions.
Zimmermann, Armin; Hotz, Thomas;
Integrating simulation and numerical analysis in the evaluation of generalized stochastic Petri nets. - In: ACM transactions on modeling and computer simulation, ISSN 1558-1195, Bd. 29 (2019), 4, S. 24:1-24:25
Semper, Sebastian; Hotz, Thomas;
Packing bounds for outer products with applications to compressive sensing. - In: Geometric science of information, (2019), S. 135-143

Eichfelder, Gabriele; Hotz, Thomas; Wieditz, Johannes;
An algorithm for computing Fréchet means on the sphere. - In: Optimization letters, ISSN 1862-4480, Bd. 13 (2019), 7, S. 1523-1533

For most optimisation methods an essential assumption is the vector space structure of the feasible set. This condition is not fulfilled if we consider optimisation problems over the sphere. We present an algorithm for solving a special global problem over the sphere, namely the determination of Fréchet means, which are points minimising the mean distance to a given set of points. The Branch and Bound method derived needs no further assumptions on the input data, but is able to cope with this objective function which is neither convex nor differentiable. The algorithms performance is tested on simulated and real data.
Semper, Sebastian; Römer, Florian; Hotz, Thomas; Del Galdo, Giovanni;
Grid-free Direction-of-Arrival estimation with compressed sensing and arbitrary antenna arrays. - In: 2018 IEEE International Conference on Acoustics, Speech, and Signal Processing, ISBN 978-1-5386-4658-8, (2018), S. 3251-3255
Semper, Sebastian; Römer, Florian; Hotz, Thomas; Del Galdo, Giovanni;
Sparsity order estimation from a single compressed observation vector. - In: IEEE transactions on signal processing, Bd. 66 (2018), 15, S. 3958-3971
Hotz, Thomas;
Hilft Honig Husten heilen?. - In: Kinderuni Ilmenau 2017, (2017)