  In light of the continuing emergence of new SARS-CoV-2 variants and vaccines,
we create a simulation framework for exploring possible infection trajectories
under various scenarios. The situations of primary interest involve the
interaction between three components: vaccination campaigns, non-pharmaceutical
interventions (NPIs), and the emergence of new SARS-CoV-2 variants.
Additionally, immunity waning and vaccine boosters are modeled to account for
their growing importance. New infections are generated according to a
hierarchical model in which people have a random, individual infectiousness.
The model thus includes super-spreading observed in the COVID-19 pandemic. Our
simulation functions as a dynamic compartment model in which an individual's
history of infection, vaccination, and possible reinfection all play a role in
their resistance to further infections. We present a risk measure for each
SARS-CoV-2 variant, $\rho^\V$, that accounts for the amount of resistance
within a population and show how this risk changes as the vaccination rate
increases. Furthermore, by considering different population compositions in
terms of previous infection and type of vaccination, we can learn about
variants which pose differential risk to different countries. Different control
strategies are implemented which aim to both suppress COVID-19 outbreaks when
they occur as well as relax restrictions when possible. We demonstrate that a
controller that responds to the effective reproduction number in addition to
case numbers is more efficient and effective in controlling new waves than
monitoring case numbers alone. This is of interest as the majority of the
public discussion and well-known statistics deal primarily with case numbers.
