  In this paper, we explore whether the infection-rate of a disease can serve
as a robust monitoring variable in epidemiological surveillance algorithms. The
infection-rate is dependent on population mixing patterns that do not vary
erratically day-to-day; in contrast, daily case-counts used in contemporary
surveillance algorithms are corrupted by reporting errors. The technical
challenge lies in estimating the latent infection-rate from case-counts. Here
we devise a Bayesian method to estimate the infection-rate across multiple
adjoining areal units, and then use it, via an anomaly detector, to discern a
change in epidemiological dynamics. We extend an existing model for estimating
the infection-rate in an areal unit by incorporating a Markov random field
model, so that we may estimate infection-rates across multiple areal units,
while preserving spatial correlations observed in the epidemiological dynamics.
To carry out the high-dimensional Bayesian inverse problem, we develop an
implementation of mean-field variational inference specific to the infection
model and integrate it with the random field model to incorporate correlations
across counties. The method is tested on estimating the COVID-19
infection-rates across all 33 counties in New Mexico using data from the summer
of 2020, and then employing them to detect the arrival of the Fall 2020
COVID-19 wave. We perform the detection using a temporal algorithm that is
applied county-by-county. We also show how the infection-rate field can be used
to cluster counties with similar epidemiological dynamics.
