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The current pandemic is a great challenge for several research areas. In addition to virology research, mathematical models and simulations can be a valuable contribution to the understanding of the dynamics of the pandemic and can give recommendations to physicians and politicians. Based on actual data of people infected with COVID-19 from the European Center for Disease Prevention and Control (ECDC), input parameters of mathematical models will be determined and applied. These parameters will be estimated for the UK, Italy, Spain, and Germany and used in an S I R -type model. As a basis for the model’s calibration, the initial exponential growth phase of the COVID-19 pandemic in the named countries is used. Strategies for the commencing and ending of social and economic shutdown measures are discussed.

Abstract. In the present paper we investigate optimal control of semiconductor melts in zone-melting and Czochralski growth configurations. The flow is governed by the Boussinesq approximation of the Navier-Stokes system. The control goal consists in tracking of a prescribed flow field. As control action boundary heating in terms of Dirichlet and Neumann-type boundary conditions is considered. Optimal control strategies are characterized in terms of the first-order optimality conditions. On the numerical level these optimality conditions are solved by a damped Picard iteration. We present numerical experiments in two and three spatial dimensions for the crystal (Bi0.25Sb0.75)2T e2, which is formed by a composition of bismuth point fifty antimony one point fifty tellurium two, as well as for Si (Silicium).