Fluctuation effects in metapopulation models: percolation and pandemic threshold

TL;DR

This paper incorporates stochastic fluctuations into metapopulation models to analytically determine disease spread thresholds, linking them to percolation theory and providing bounds for pandemic thresholds across various networks.

Contribution

It introduces a stochastic approach to metapopulation models, enabling analytical calculation of disease thresholds and their relation to percolation theory.

Findings

Global disease spread is described by bond percolation on the network.

Provides a lower bound estimate for the pandemic threshold in SIR models.

Analytical methods apply to all network types and model parameters.

Abstract

Metapopulation models provide the theoretical framework for describing disease spread between different populations connected by a network. In particular, these models are at the basis of most simulations of pandemic spread. They are usually studied at the mean-field level by neglecting fluctuations. Here we include fluctuations in the models by adopting fully stochastic descriptions of the corresponding processes. This level of description allows to address analytically, in the SIS and SIR cases, problems such as the existence and the calculation of an effective threshold for the spread of a disease at a global level. We show that the possibility of the spread at the global level is described in terms of (bond) percolation on the network. This mapping enables us to give an estimate (lower bound) for the pandemic threshold in the SIR case for all values of the model parameters and for all possible networks.