  Comparing how different populations have suffered under COVID-19 is a core
part of ongoing investigations into how public policy and social inequalities
influence the number of and severity of COVID-19 cases. But COVID-19 incidence
can vary multifold from one subpopulation to another, including between
neighborhoods of the same city, making comparisons of case rates deceptive. At
the same time, although epidemiological heterogeneities are increasingly
well-represented in mathematical models of disease spread, fitting these models
to real data on case numbers presents a tremendous challenge, as does
interpreting the models to answer questions such as: Which public health
policies achieve the best outcomes? Which social sacrifices are most worth
making? Here we compare COVID-19 case-curves between different US states, by
clustering case surges between March 2020 and March 2021 into groups with
similar dynamics. We advance the hypothesis that each surge is driven by a
subpopulation of COVID-19 contacting individuals, and make detecting the size
of that population a step within our clustering algorithm. Clustering reveals
that case trajectories in each state conform to one of a small number (4-6) of
archetypal dynamics. Our results suggest that while the spread of COVID-19 in
different states is heterogeneous, there are underlying universalities in the
spread of the disease that may yet be predictable by models with reduced
mathematical complexity. These universalities also prove to be surprisingly
robust to school closures, which we choose as a common, but high social cost,
public health measure.
