Physics – Condensed Matter – Disordered Systems and Neural Networks
Scientific paper
2010-04-09
Journal of Theoretical Biology 267:554-564 (2010)
Physics
Condensed Matter
Disordered Systems and Neural Networks
14 pages, 13 figures, final version
Scientific paper
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.
Barthelemy Marc
Godreche Claude
Luck Jean-Marc
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