Mean-field models for non-Markovian epidemics on networks

Sherborne, Neil, Miller, Joel C, Blyuss, Konstantin B and Kiss, Istvan Z (2017) Mean-field models for non-Markovian epidemics on networks. Journal of Mathematical Biology. ISSN 0303-6812

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Abstract

This paper introduces a novel extension of the edge-based compartmental model to epidemics where the transmission and recovery processes are driven by general independent probability distributions. Edge-based compartmental modelling is just one of many different approaches used to model the spread of an infectious disease on a network; the major result of this paper is the rigorous proof that the edge-based compartmental model and the message passing models are equivalent for general independent transmission and recovery processes. This implies that the new model is exact on the ensemble of configuration model networks of infinite size. For the case of Markovian transmission themessage passing model is re-parametrised into a pairwise-like model which is then used to derive many well-known pairwise models for regular networks, or when the infectious period is exponentially distributed or is of a fixed length.

Item Type: Article
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Research Centres and Groups: Mathematical Physics Group
Subjects: Q Science > QA Mathematics
Depositing User: Konstantin Blyuss
Date Deposited: 12 Oct 2017 14:46
Last Modified: 12 Oct 2017 14:46
URI: http://sro.sussex.ac.uk/id/eprint/70503

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