Individual risk-aversion responses tune epidemics to critical transmissibility ($R=1$)

TL;DR

This paper introduces a stochastic epidemic model showing how individual risk responses can naturally lead to multiple infection waves and keep the effective reproduction number near the critical value of 1, without external intervention.

Contribution

The study presents a novel model demonstrating how uncoordinated individual risk behaviors can self-organize epidemic dynamics around the critical transmissibility threshold.

Findings

Multiple infection waves emerge without external modulation.

The effective reproduction number tends to stabilize around R=1.

Individual risk propensities evolve towards a specific distribution.

Abstract

Changes in human behavior are increasingly recognized as a major determinant of epidemic dynamics. Although collective activity can be modified through imposed measures to control epidemic progression, spontaneous changes can also arise as a result of uncoordinated individual responses to the perceived risk of contagion. Here we introduce a stochastic epidemic model that implements population responses driven by individual- and time-dependent risk-taking propensity. The model reveals an emergent mechanism for the generation of multiple infection waves of decreasing amplitude without the need to consider external modulation of parameters. Successive waves tune the effective reproduction number to its critical value $R=1$. This process is a consequence of the interplay of the fractions of susceptible and infected population and the average risk-taking propensity, as shown by a mean-field approach. The proposed mechanism also shows how, under the threat of contagion, the distribution of individual risk propensities evolves towards a well-defined profile. Successive waves trigger selective sweeps of risk-taking propensity at a pace determined by individual risk reaction rates. This kind of collective, self-generated pressure, may therefore shape risk-aversion profiles associated to epidemics in human groups. The final state is self-organized and generic, independent of the parameter values. We conclude that uncoordinated changes in human behavior can, by themselves, explain major qualitative and quantitative features of the epidemic process, as the emergence of multiple waves and the tendency to remain around $R=1$ observed worldwide after the first few waves of COVID-19.