title: Pair-level approximations to the spatio-temporal dynamics of epidemics on asymmetric contact networks.
abstract: The process of infection during an epidemic can be envisaged as being transmitted via a network of routes represented by a contact network. Most differential equation models of epidemics are mean-field models. These contain none of the underlying spatial structure of the contact network. By extending the mean-field models to pair-level, some of the spatial structure can be contained in the model. Some networks of transmission such as river or transportation networks are clearly asymmetric, whereas others such as airborne infection can be regarded as symmetric. Pair-level models have been developed to describe symmetric contact networks. Here we report on work to develop a pair-level model that is also applicable to asymmetric contact networks. The procedure for closing the model at the level of pairs is discussed in detail. The model is compared against stochastic simulations of epidemics on asymmetric contact networks and against the predictions of the symmetric model on the same networks.
authors.affiliation: Division of Applied Mathematics, Department of Mathematical Sciences, M&O Building, The University of Liverpool, L69 7ZL, United Kingdom. k.j.sharkey@liv.ac.uk
authors.forename: Kieran J
authors.initials: KJ
authors.lastname: Sharkey
authors.forename: Carmen
authors.initials: C
authors.lastname: Fernandez
authors.forename: Kenton L
authors.initials: KL
authors.lastname: Morgan
authors.forename: Edmund
authors.initials: E
authors.lastname: Peeler
authors.forename: Mark
authors.initials: M
authors.lastname: Thrush
authors.forename: James F
authors.initials: JF
authors.lastname: Turnbull
authors.forename: Roger G
authors.initials: RG
authors.lastname: Bowers
mesh_terms: D003141:Communicable Diseases / Q000453:epidemiology / Q000635:transmission*; D003198:Computer Simulation; D004196:Disease Outbreaks; D008954:Models, Biological; D013269:Stochastic Processes