  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.
