  For the description of a pandemic mathematical models could be interesting.
Both for physicians and politicians as a base for decisions to treat the
disease. The responsible estimation of parameters is a main issue of
mathematical pandemic models. Especially a good choice of $\beta$ as the number
of others that one infected person encounters per unit time (per day)
influences the adequateness of the results of the model. For the actual
COVID-19 pandemic some aspects of the parameter choice will be discussed.
Because of the incompatibility of the data of the Johns-Hopkins-University to
the data of the German Robert-Koch-Institut we use the COVID-19 data of the
European Centre for Disease Prevention and Control (ECDC) as a base for the
parameter estimation. Two different mathematical methods for the data analysis
will be discussed in this paper and possible sources of trouble will be shown.
As example of the parameter choice serve the data of the USA and the UK. The
resulting parameters will be used estimated and used in W.\,O. Kermack and
A.\,G. McKendrick's SIR model. Strategies for the commencing and ending of
social and economic shutdown measures are discussed. The numerical solution of
the ordinary differential equation system of the modified SIR model is being
done with a Runge-Kutta integration method of fourth order. At the end the
applicability of the SIR model could be shown essentially. Suggestions about
appropriate points in time at which to commence with lockdown measures based on
the acceleration rate of infections conclude the paper.
