Jahresber Dtsch Math Ver
2020[]; 122
(3
): 167-205
PMID38624403
show ga
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.
SUPPLEMENTARY INFORMATION: The online version of this article
(10.1365/s13291-020-00219-9) contains supplementary material, which is available
to authorized users.
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