title: Rapid simulation of spatial epidemics: a spectral method.
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.
authors: Department of Life Sciences, University of Warwick, Gibbet Hill Rd, Coventry CV4 7AL, United Kingdom. Electronic address: S.Brand@warwick.ac.uk.
authors: Samuel P C
authors: SP
authors: Brand
authors: Mathematics Institute, University of Warwick, Gibbet Hill Rd, Coventry CV4 7AL, United Kingdom.
authors: Michael J
authors: MJ
authors: Tildesley
authors: Department of Life Sciences, University of Warwick, Gibbet Hill Rd, Coventry CV4 7AL, United Kingdom; Mathematics Institute, University of Warwick, Gibbet Hill Rd, Coventry CV4 7AL, United Kingdom.
authors: Matthew J
authors: MJ
authors: Keeling
mesh_terms: D000465:Algorithms; D000818:Animals; D002417:Cattle; D003141:Communicable Diseases / Q000453:epidemiology / Q000662:veterinary; D003198:Computer Simulation; D058872:Epidemics / Q000662:veterinary; D006801:Humans; D016013:Likelihood Functions; D008954:Models, Biological; D013997:Time Factors
keywords: Accelerated Simulation; Cattle infections; Outbreak forecasting