Non-Analytic Behaviour in Large-deviations of the SIR model under the influence of Lockdowns

TL;DR

This study uses large-deviation techniques to analyze the impact of lockdowns on the SIR model's infection spread on Small-World networks, revealing non-analytic behaviors and phase transitions.

Contribution

It introduces a numerical approach combining the Wang-Landau algorithm with network lockdown simulations to fully characterize the SIR model's infection distribution.

Findings

Discovered non-analytic points in the infection distribution.

Identified discontinuous transitions in outbreak metrics.

Confirmed the validity of the large-deviation principle for the system.

Abstract

We numerically investigate the dynamics of an SIR model with infection level-based lockdowns on Small-World networks. Using a large-deviation approach, namely the Wang-Landau algorithm, we study the distribution of the cumulative fraction of infected individuals. We are able to resolve the density of states for values as low as $10^{-85}$. Hence, we measure the distribution on its full support giving a complete characterization of this quantity. The lockdowns are implemented by severing a certain fraction of the edges in the Small-World network, and are initiated and released at different levels of infection, which are varied within this study. We observe points of non-analytical behaviour for the pdf and discontinuous transitions for correlations with other quantities such as the maximum fraction of infected and the duration of outbreaks. Further, empirical rate functions were calculated for different system sizes, for which a convergence is clearly visible indicating that the large-deviation principle is valid for the system with lockdowns.