  Successful predictive modeling of epidemics requires an understanding of the
implicit feedback control strategies which are implemented by populations to
modulate the spread of contagion. While this task of capturing endogenous
behavior can be achieved through intricate modeling assumptions, we find that a
population's reaction to case counts can be described through a second order
affine dynamical system with linear control which fits well to the data across
different regions and times throughout the COVID-19 pandemic. The model fits
the data well both in and out of sample across the 50 states of the United
States, with comparable $R^2$ scores to state of the art ensemble predictions.
In contrast to recent models of epidemics, rather than assuming that
individuals directly control the contact rate which governs the spread of
disease, we assume that individuals control the rate at which they vary their
number of interactions, i.e. they control the derivative of the contact rate.
We propose an implicit feedback law for this control input and verify that it
correlates with policies taken throughout the pandemic. A key takeaway of the
dynamical model is that the "stable" point of case counts is non-zero, i.e.
COVID-19 will not be eradicated under the current collection of policies and
strategies, and additional policies are needed to fully eradicate it quickly.
Hence, we suggest alternative implicit policies which focus on making
interventions (such as vaccinations and mobility restrictions) a function of
cumulative case counts, for which our results suggest a better possibility of
eradicating COVID-19.
