Summary: This is an analysis of the COVID-19 pandemic by comparably simple mathematical and numerical methods. The final goal is to predict the peak of the epidemic outbreak per country with a reliable technique. The difference to other modelling approaches is to stay extremely close to the available data, using as few hypotheses and parameters as possible.
For the convenience of readers, the basic notions of modelling epidemics are collected first, focusing on the standard SIR model. Proofs of various properties of the model are included. But such models are not directly compatible with available data. Therefore a special variation of a SIR model is presented that directly works with the data provided by the Johns Hopkins University. It allows to monitor the registered part of the pandemic, but is unable to deal with the hidden part. To reconstruct data for the unregistered Infected, a second model uses current experimental values of the infection fatality rate and a data-driven estimation of a specific form of the recovery rate. All other ingredients are data-driven as well. This model allows predictions of infection peaks.
Various examples of predictions are provided for illustration. They show what countries have to face that are still expecting their infection peak. Running the model on earlier data shows how closely the predictions follow the transition from an uncontrolled outbreak to the mitigation situation by non-pharmaceutical interventions like contact restrictions.