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Since the first identified case of COVID-19 in Wuhan, China, the disease has developed into a pandemic, imposing a major challenge for health authorities and hospitals worldwide. Mathematical transmission models can help hospitals to anticipate and prepare for an upcoming wave of patients by forecasting the time and severity of infections. Taking the city of Heidelberg as an example, we predict the ongoing spread of the disease for the next months including hospital and ventilator capacity and consider the possible impact of currently imposed countermeasures.