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

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