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?:abstract
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The present study investigates essential steps in build‐up of models for description of the spread of infectious diseases. Combining these modules, a SEI(3)RSD model will be developed, which can take into account a possible passive immunisation by vaccination as well as different durations of latent and incubation periods. Besides, infectious persons with and without symptoms can be distinguished. Due to the current world‐wide SARS‐CoV‐2 pandemic (COVID‐19 pandemic) models for description of the spread of infectious diseases and their application for forecasts have become into the focus of the scientific community as well as of broad public more than usual. Currently, many papers and studies have appeared and appear dealing with the virus SARS‐CoV‐2 and the COVID‐19 disease caused by it. This occurs under medical, virological, economic, sociological and further aspects as well as under mathematical points of view. Concerning the last‐mentioned point, the main focus lies on the application of existing models and their adaptation to data about the course of infection available at the current time. Clearly, the aim is to predict the possible further development, for instance in Germany. It is of particular interest to investigate how will be the influence of political and administrative measures like contact restrictions, closing or rather re‐opening of schools, restaurants, hotels etc. on the course of infection. The steps considered here for building up suitable models are well‐known for long time. However, understandably they will not be dealt with in an extended way in current application‐oriented works. Therefore, it is the aim of this study to present some existing steps of modelling without any pretension of completeness. Thus, on the one hand we give assistance and, on the other hand, we develop a model capable to take already known properties of COVID‐19 as well as a later possible passive immunisation by vaccination and a possible loss of immunity of recovered persons into account.
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