Homeostatic behavioural response to COVID-19 infections returns R to a set-point of 1

TL;DR

This paper presents a simple model showing that people's behavioral responses during COVID-19 lead to the reproduction number stabilizing around 1, with infection changes following a Cauchy distribution, supported by worldwide data analysis.

Contribution

It introduces a homeostatic behavioral model predicting R stabilizes at 1 and demonstrates this with empirical COVID-19 data analysis.

Findings

Reproduction rate R has a median of 1 worldwide.

Relative change in infections follows a standard Cauchy distribution.

Behavioral responses influence infection dynamics.

Abstract

One clear aspect of behaviour in the COVID-19 pandemic has been people's focus on, and response to, reported or observed infection numbers in their community. We describe a simple model of infectious disease spread in a pandemic situation where people's behaviour is influenced by the current risk of infection and where this behavioural response acts homeostatically to return infection risk to a certain preferred level. This model predicts that the reproduction rate $R$ will be centered around a median value of 1, and that a related measure of relative change in the number of new infections will follow the standard Cauchy distribution. Analysis of worldwide COVID-19 data shows that the estimated reproduction rate has a median of 1, and that this measure of relative change calculated from reported numbers of new infections closely follows the standard Cauchy distribution at both an overall and an individual country level.