Discontinuous transitions of social distancing in SIR model

TL;DR

This paper extends the SIR epidemiological model to include social distancing behaviors, predicting multiple discontinuous transitions akin to phase changes, supported by data from COVID-19 waves in Austria, Israel, and Germany.

Contribution

It introduces a novel extension of the SIR model that captures discontinuous social distancing transitions, linking epidemiology with phase transition theory.

Findings

Model predicts multiple second-order phase transitions in social distancing.

Data from COVID-19 waves support the model's predictions.

Provides analytical tools for analyzing pandemic wave dynamics.

Abstract

To describe the dynamics of social distancing during pandemics, we follow previous efforts to combine basic epidemiology models (e.g. SIR - Susceptible, Infected, and Recovered) with game and economy theory tools. We present an extension of the SIR model that predicts a series of discontinuous transitions in social distancing. Each transition resembles a phase transition of the second-order (Ginzburg-Landau instability) and, therefore, potentially a general phenomenon. The first wave of COVID-19 led to social distancing around the globe: severe lockdowns to stop the pandemic were followed by a series of lockdown lifts. Data analysis of the first wave in Austria, Israel, and Germany corroborates the soundness of the model. Furthermore, this work presents analytical tools to analyze pandemic waves, which may be extended to calculate derivatives of giant components in network percolation transitions and may also be of interest in the context of crisis formation theories.