Before revision:  We explain the setup of the Kermack-McKendrick theory (passing to a discrete approach) and use medical information to derive a different model which we call {\em adapted K-McK-model}.
After revision:  We explain the setup of the Kermack-McKendrick theory (passing to a discrete approach) and use medical information for specializing to a model which we call {\em adapted K-McK-model}.