Current Implicit Policies May Not Eradicate COVID-19

TL;DR

This paper models population responses to COVID-19 using a second order affine dynamical system with linear control, revealing that current policies are insufficient for eradication and suggesting alternative strategies based on cumulative case counts.

Contribution

It introduces a novel dynamical model of implicit feedback control in epidemic spread, emphasizing the derivative of contact rate control and its relation to policies.

Findings

Model fits COVID-19 data across US states with high accuracy.

Current policies stabilize case counts at a non-zero level.

Alternative policies based on cumulative cases may enable eradication.

Abstract

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.