Brand, Samuel, Tildesley, Michael J. and Keeling, Matthew James (2015) Rapid simulation of spatial epidemics : a spectral method. Journal of Theoretical Biology, Volume 370 . pp. 121-134. doi:10.1016/j.jtbi.2015.01.027 ISSN 0022-5193.

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Abstract

Spatial structure and hence the spatial position of host populations plays a vital role in the spread of infection. In the majority of situations, it is only possible to predict the spatial spread of infection using simulation models, which can be computationally demanding especially for large population sizes. Here we develop an approximation method that vastly reduces this computational burden. We assume that the transmission rates between individuals or sub-populations are determined by a spatial transmission kernel. This kernel is assumed to be isotropic, such that the transmission rate is simply a function of the distance between susceptible and infectious individuals; as such this provides the ideal mechanism for modelling localised transmission in a spatial environment. We show that the spatial force of infection acting on all susceptibles can be represented as a spatial convolution between the transmission kernel and a spatially extended ‘image’ of the infection state. This representation allows the rapid calculation of stochastic rates of infection using fast-Fourier transform (FFT) routines, which greatly improves the computational efficiency of spatial simulations. We demonstrate the efficiency and accuracy of this fast spectral rate recalculation (FSR) method with two examples: an idealised scenario simulating an SIR-type epidemic outbreak amongst N habitats distributed across a two-dimensional plane; the spread of infection between US cattle farms, illustrating that the FSR method makes continental-scale outbreak forecasting feasible with desktop processing power. The latter model demonstrates which areas of the US are at consistently high risk for cattle-infections, although predictions of epidemic size are highly dependent on assumptions about the tail of the transmission kernel.

Item Type:	Journal Article
Divisions:	Faculty of Science, Engineering and Medicine > Science > Life Sciences (2010- ) Faculty of Science, Engineering and Medicine > Science > Mathematics
Journal or Publication Title:	Journal of Theoretical Biology
Publisher:	Elsevier
ISSN:	0022-5193
Official Date:	7 April 2015
Dates:	Date Event 7 April 2015 Published 4 February 2015 Available 26 January 2015 Accepted 19 August 2014 Submitted
Volume:	Volume 370
Page Range:	pp. 121-134
DOI:	10.1016/j.jtbi.2015.01.027
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access
Date of first compliant deposit:	6 June 2016
Date of first compliant Open Access:	6 June 2016

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