Discrete-time moment closure models for epidemic spreading in populations of interacting individuals

Frasca, Mattia and Sharkey, Kieran J ORCID: 0000-0002-7210-9246 (2016) Discrete-time moment closure models for epidemic spreading in populations of interacting individuals. JOURNAL OF THEORETICAL BIOLOGY, 399. pp. 13-21.

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Abstract

Understanding the dynamics of spread of infectious diseases between individuals is essential for forecasting the evolution of an epidemic outbreak or for defining intervention policies. The problem is addressed by many approaches including stochastic and deterministic models formulated at diverse scales (individuals, populations) and different levels of detail. Here we consider discrete-time SIR (susceptible-infectious-removed) dynamics propagated on contact networks. We derive a novel set of 'discrete-time moment equations' for the probability of the system states at the level of individual nodes and pairs of nodes. These equations form a set which we close by introducing appropriate approximations of the joint probabilities appearing in them. For the example case of SIR processes, we formulate two types of model, one assuming statistical independence at the level of individuals and one at the level of pairs. From the pair-based model we then derive a model at the level of the population which captures the behavior of epidemics on homogeneous random networks. With respect to their continuous-time counterparts, the models include a larger number of possible transitions from one state to another and joint probabilities with a larger number of individuals. The approach is validated through numerical simulation over different network topologies.

Item Type:	Article
Uncontrolled Keywords:	Epidemics, Mathematical models, SIR processes
Depositing User:	Symplectic Admin
Date Deposited:	24 Mar 2017 15:56
Last Modified:	19 Jan 2023 07:25
DOI:	10.1016/j.jtbi.2016.03.024
Related URLs:	Author Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3004472