  In this work we look at several mathematical models that have been
constructed during the present pandemic to address dfferent issues of
importance to public health policies about epidemic scenarios and thier causes.
We start by briefly reviewing the most basic properties of the classic
Kermack-McKendrick models and then proceed to look at some generalizations and
their applications to contact structures, cocirculation of viral infections,
growth patterns of epidemic curves, characterization of probability
distributions and passage times necessary to parametrize the compartments that
are added to the basic Kermack-McKendrick model. All of these examples revolve
around the idea that a system of differential equations constructed for an
specifc epidemiological problem, has as central and main theoretical and
conceptual support the epidemiological, medical and biological context that
motivates its construction and analysis. Fitting differential models to data
without a sound perspective on the biological feasibility of the mathematical
model will provide an statistical significant fit but will also fall short of
providing useful information for the management, mitigation and eventual
control of the epidemic of SARS-CoV-2.
