  The main focus of this chapter is on public health control strategies which
are currently the main way to mitigate COVID-19 pandemic. We introduce and
compare compartmental models of increasing complexity for COVID-19 transmission
to describe dynamics of the disease spread. We begin by considering an SEAIR
model including basic characteristics related to COVID-19. Next, we shall pay
attention to age-structure modeling to emphasis the role of age-group
individuals on the disease spread. A Model with constant delay is also
formulated to show the impact of the latency period on the severity of
COVID-19. Since there is evidence that for COVID-19 disease, important
relationships exist between what is happening in the host and what is occurring
at the population level, we shall link the basic model to in-host dynamics
through the so-called threshold-type delay models. Finally, we will include
demographic effects to the most complex models and we will conduct rigorous
bifurcation analysis to quantify possible factors responsible for disease
progression.
