Need for speed: An optimized gridding approach for spatially explicit disease simulations.

Stefan Sellman,Michael J Tildesley,Tom Lindström,Uno Wennergren,Matt J Keeling,Peter Brommesson,Colleen T Webb,Kimberly Tsao,Mark M Tanaka

doi:10.1371/journal.pcbi.1006086

Stefan Sellman, Michael J Tildesley + Show 7 more

Open Access

https://doi.org/10.1371/journal.pcbi.1006086

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Abstract

Numerical models for simulating outbreaks of infectious diseases are powerful tools for informing surveillance and control strategy decisions. However, large-scale spatially explicit models can be limited by the amount of computational resources they require, which poses a problem when multiple scenarios need to be explored to provide policy recommendations. We introduce an easily implemented method that can reduce computation time in a standard Susceptible-Exposed-Infectious-Removed (SEIR) model without introducing any further approximations or truncations. It is based on a hierarchical infection process that operates on entire groups of spatially related nodes (cells in a grid) in order to efficiently filter out large volumes of susceptible nodes that would otherwise have required expensive calculations. After the filtering of the cells, only a subset of the nodes that were originally at risk are then evaluated for actual infection. The increase in efficiency is sensitive to the exact configuration of the grid, and we describe a simple method to find an estimate of the optimal configuration of a given landscape as well as a method to partition the landscape into a grid configuration. To investigate its efficiency, we compare the introduced methods to other algorithms and evaluate computation time, focusing on simulated outbreaks of foot-and-mouth disease (FMD) on the farm population of the USA, the UK and Sweden, as well as on three randomly generated populations with varying degree of clustering. The introduced method provided up to 500 times faster calculations than pairwise computation, and consistently performed as well or better than other available methods. This enables large scale, spatially explicit simulations such as for the entire continental USA without sacrificing realism or predictive power.

Highlights

Models of infectious diseases are powerful tools for studying outbreak dynamics
We find that our optimization techniques works well, and when the introduced algorithms are implemented with these optimizations, computation time can be reduced by more than two orders of magnitude compared to pairwise calculations
We investigate how this algorithm compares to simulations based on both the pairwise algorithm, the conditional entry algorithm presented by Keeling and Rohani [11], and the fast spectral rate recalculation (FSR) algorithm introduced by Brand et al [10]

Summary

Introduction

Models of infectious diseases are powerful tools for studying outbreak dynamics. Mass action mixing models assume equal probability of infection among all individuals in a population and have provided important theoretical insights for epidemiology. The importance of deviations from this assumption is largely recognized [1], and researchers are increasingly implementing stochastic simulation models that incorporate various levels of realism [2]. The effect of spatial heterogeneity can have a pronounced effect on outbreak dynamics [3] and is of particular concern when models are used to inform policy. We focus on livestock disease models, but emphasize that the proposed methods are very broadly applicable. Livestock models typically consider infections at the farm level [5], and since the farms have fixed spatial locations, spatially explicit models are appropriate. Distance dependent transmission is commonly modeled with a spatial kernel that describes how transmission risk varies with distance [5,6,7]

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