Large-deviations of disease spreading dynamics with vaccination.

We numerically simulated the spread of disease for a Susceptible-Infected-Recovered (SIR) model on contact networks drawn from a small-world ensemble. We investigated the impact of two types of vaccination strategies, namely random vaccination and high-degree heuristics, on the probability density function (pdf) of the cumulative number C of infected people over a large range of its support. To obtain the pdf even in the range of probabilities as small as 10-80, we applied a large-deviation approach, in particular the 1/t Wang-Landau algorithm. To study the size-dependence of the pdfs within the framework of large-deviation theory, we analyzed the empirical rate function. To find out how typical as well as extreme mild or extreme severe infection courses arise, we investigated the structures of the time series conditioned to the observed values of C.