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SIR models are mathematical models that can be used to quantitatively describe the onset, spread and extinction of epidemic infectious diseases. They consist of chained differential or difference equations. In the early phase of the Covid-19 pandemic, SIR models were used to model the course of the infection and estimate the likely success of possible control measures. The equations of the SIR models can be solved numerically and then provide bell curves or saturation curves, which can be hyperbolic or sigmoid, depending on the variables considered and the basic requirements. A single wave of infection can be easily simulated with the SIR basic model. However, Covid-19 is a succession of infection outbreaks, with several, sometimes overlapping, waves of infection following each other, which are caused by different types of viruses that emerged from their predecessors through mutations. This behaviour cannot be reproduced by conventional SIR models. This describes how the SIR basic model can be expanded so that it reflects the overall course of the corona pandemic in Germany.

The results show that the model can depict the course of infections and deaths, with no systematic deviation from the data in the course of infections and only a slight systematic deviation in the development of deaths. Its informative value goes beyond simply tracing the course of the epidemic. It confirms the plausibility of the basic assumptions made about the mechanism of disease spread. It provides epidemiological indicators such as morbidity and mortality with which the different virus variants that cause the disease can be compared and with which the pandemic as a whole can be characterized and classified in comparison to other causes of death. It is able to narrow down the temporal origin of Covid-19 and retrospectively provides an evidence-based assessment of the success of pandemic control by showing how protective measures must change the morbidity and mortality kinetics of the pandemic if they are effective.

Ekkehard Kuhn

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