  There are many sources of data giving information about the number of
SARS-CoV-2 infections in the population, but all have major drawbacks,
including biases and delayed reporting. For example, the number of confirmed
cases largely underestimates the number of infections, deaths lag infections
substantially, while test positivity rates tend to greatly overestimate
prevalence. Representative random prevalence surveys, the only putatively
unbiased source, are sparse in time and space, and the results come with a big
delay. Reliable estimates of population prevalence are necessary for
understanding the spread of the virus and the effects of mitigation strategies.
We develop a simple Bayesian framework to estimate viral prevalence by
combining the main available data sources. It is based on a discrete-time SIR
model with time-varying reproductive parameter. Our model includes likelihood
components that incorporate data of deaths due to the virus, confirmed cases,
and the number of tests administered on each day. We anchor our inference with
data from random sample testing surveys in Indiana and Ohio. We use the results
from these two states to calibrate the model on positive test counts and
proceed to estimate the infection fatality rate and the number of new
infections on each day in each state in the USA. We estimate the extent to
which reported COVID cases have underestimated true infection counts, which was
large, especially in the first months of the pandemic. We explore the
implications of our results for progress towards herd immunity.
