Large-deviations of the SIR model around the epidemic threshold

  title={Large-deviations of the SIR model around the epidemic threshold},
  author={Yannick Feld and Alexander K. Hartmann},
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… 



SIR dynamics in random networks with communities

For large-scale epidemics, strengthening the community structure to reduce the size of disease is undoubtedly an effective way, and this paper establishes a susceptible–infected–recovered (SIR) model in a two-community network with an arbitrary joint degree distribution, formulated as a probability generating function.

Predicting the epidemic threshold of the susceptible-infected-recovered model

In most of the networks with positive degree-degree correlations, an eigenvector localized on the high k-core nodes, or a high level of clustering, the epidemic threshold predicted by the MFL method, which uses the degree distribution as the only input information, performs better than the other two methods.

Spread of epidemic disease on networks.

  • M. Newman
  • Mathematics
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2002
This paper shows that a large class of standard epidemiological models, the so-called susceptible/infective/removed (SIR) models can be solved exactly on a wide variety of networks.

Epidemic dynamics on an adaptive network.

This work proposes a low-dimensional model to describe the epidemic dynamics on an adaptive network, where the susceptibles are able to avoid contact with the infected by rewiring their network connections, and presents a full local bifurcation analysis.


We study infection spread in continuous time SIRS epidemic models. When infection is supercritical, the proportions of susceptible and infected individuals in the population tend to stabilize near an

Discrete-time Markov chain approach to contact-based disease spreading in complex networks

Many epidemic processes in networks spread by stochastic contacts among their connected vertices. There are two limiting cases widely analyzed in the physics literature, the so-called contact process

Modelling disease outbreaks in realistic urban social networks

The results suggest that outbreaks can be contained by a strategy of targeted vaccination combined with early detection without resorting to mass vaccination of a population.

Rare-event properties of the Nagel-Schreckenberg model.

A large-deviation approach was applied to the distribution of traffic flow q for the Nagel-Schreckenberg model, which allowed for characterize the flow distribution over a large range of the support and identify the characteristics of rare and even very rare traffic situations.

On the properties of small-world network models

Abstract:We study the small-world networks recently introduced by Watts and Strogatz [Nature 393, 440 (1998)], using analytical as well as numerical tools. We characterize the geometrical properties