Large-deviations of the SIR model around the epidemic threshold

Abstract

We numerically study the dynamics of the SIR disease model on small-world networks by using a large-deviation approach. This allows us to obtain the probability density function of the total fraction of infected nodes and of the maximum fraction of simultaneously infected nodes down to very small probability densities like $10^{-2500}$. We analyze the structure of the disease dynamics and observed three regimes in all probability density functions, which correspond to quick mild, quick extremely severe and sustained severe dynamical evolutions, respectively. Furthermore, the mathematical rate functions of the densities are investigated. The results indicate that the so called large-deviation property hold for the SIR model. Finally, we measured correlations with other quantities like the duration of an outbreak or the peak position of the fraction of infections, also in the rare regions which are not accessible by standard simulation techniques.

References in corpus (7)

• The large deviation approach to statistical mechanics
• Statistical physics of vaccination
• Unification of theoretical approaches for epidemic spreading on complex networks
• A numerical approach to large deviations in continuous-time
• Finite-temperature critical point of a glass transition
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• Analysis of the convergence of the 1/t and Wang-Landau algorithms in the calculation of multidimensional integrals

Cited by in corpus (2)

• Numerical Aspects of Large Deviations
• Universal features of epidemic and vaccine models