  We are asking: why are the dynamics and control of Covid-19 most interesting
for mathematicians and why are mathematicians urgently needed for controlling
the pandemic?
  First we present our comments in a Bottom-up approach, i.e., following the
events from their beginning as they evolved through time. They happened
differently in different countries, and the main objective of the first part is
to compare these evolutions in a few selected countries with each other.
  The second part of the article is not "country-oriented" but
"problem-oriented". From a given problem we go Top-down to its solutions and
their applications in concrete situations. We have organized this part by the
mathematical methods that play a role in their solution. We give an overview of
the main branches of mathematics that play a role and sketch the most frequent
applications, emphasising mathematical pattern analysis in laboratory work and
statistical-mathematical models in judging the quality of tests; demographic
methods in the collection of data; different ways to model the evolution of the
pandemic mathematically; and clinical epidemiology in attempts to develop a
vaccine.
