Improving the computational efficiency of an agent-based spatiotemporal model of livestock disease spread and control

https://doi.org/10.1016/j.envsoft.2015.11.015Get rights and content

Highlights

  • A hybrid model architecture that combines equation-based and agent-based modelling.

  • Asynchronous software architecture featuring lightweight agents in an active concurrent environment.

  • Uniform grid-based spatial indexing in lieu of R-Tree-over-GiST spatial indexing.

Abstract

Agent-based models (ABMs) are well suited to representing the spatiotemporal spread and control of disease in a population. The explicit modelling of individuals in a large population, however, can be computationally intensive, especially when models are stochastic and/or spatially-explicit. Large-scale ABMs often require a highly parallel platform such as a high-performance computing cluster, which tends to confine their utility to university, defence and scientific research environments. This poses a challenge for those interested in modelling the spread of disease on a large scale with access only to modest hardware platforms.

The Australian Animal DISease (AADIS) model is a spatiotemporal ABM of livestock disease spread and control. The AADIS ABM is able to complete complex national-scale simulations of disease spread and control on a personal computer. Computational efficiency is achieved through a hybrid model architecture that embeds equation-based models inside herd agents, an asynchronous software architecture, and a grid-based spatial indexing scheme.

Introduction

Mathematical models of disease spread have been in use since at least the 18th century (Dietz and Heesterbeek, 2002). An example is a Susceptible, Exposed, Infectious and Recovered (SEIR) compartmental equation-based model (EBM) that uses a system of ordinary differential equations (ODEs) to predict infection state proportions in a population over time (Keeling and Rohani, 2008). The population is dynamically disaggregated into the SEIR compartments; however, individuals within any particular compartment are indistinguishable. Models such as this are termed population-based, in that top-down population-level relationships provide insight into individual-level states. Population-based models can be concise and computationally efficient, but generally assume homogeneous contact rates and susceptibility, i.e., individuals mix uniformly and randomly, and have an equal likelihood of contracting a disease. The homogeneous 'well-mixed' assumption of an aggregated population-based model is a limitation if the population is heterogeneous and mixes heterogeneously (Hethcote, 2000, Keeling et al., 2001, Kitching et al., 2006, Bansal et al., 2007, Grassly and Fraser, 2008).

Agent-based models of disease spread are formulated from the bottom-up, whereby population-level relationships emerge organically from the aggregation of individual-level behaviours. Agent-based models are well suited to capturing population heterogeneity, stochasticity, spatial relationships, adaptivity, social systems and policy elements (Parunak et al., 1998, Davidsson, 2001, Hare and Deadman, 2004, Crooks and Heppenstall, 2012). The explicit modelling of individuals in a population, however, can be computationally intensive, especially for large populations. Computational efficiency is important for models that employ Markov chain Monte-Carlo (MCMC) methods (Hamra et al., 2013). A stochastic model may be called upon to re-run a scenario with the same initial conditions thousands of times to allow trends to emerge from the underlying probabilistic mechanisms (Driels and Shin, 2004). Spatiotemporal models have additional computational challenges of efficiently managing spatial objects, spatial relationships and spatial queries (Kennedy et al., 2009). Large-scale agent-based models can require custom software implementations (Parker and Epstein, 2011), and highly parallel platforms such as high-performance computing (HPC) clusters (Carley et al., 2006, Germann et al., 2006) or general purpose computing on graphics processing units (Lysenko and D'Souza, 2008, D'Souza et al., 2009, Welch et al., 2014). Access to HPC clusters is largely in the hands of university, defence and scientific research organisations. This poses a challenge for those interested in modelling the spread of disease efficiently on a large scale with access to only standard hardware platforms.

Epidemiological models are used in Australia to support planning and policy development for exotic animal diseases such as foot-and-mouth disease (FMD) (Garner et al., 2007, Garner et al., 2014, Roche et al., 2014). FMD is a highly contagious disease of cloven-hoofed animals that significantly impacts livestock production and trade in livestock and livestock products (Buetre et al., 2013). Modelling the spread and control of FMD is complex as the virus has multiple serotypes, and spreads via multiple pathways (direct contacts, indirect contacts and aerosol plumes), to multiple host species (including cattle, sheep, goats and pigs). The environment of a potential outbreak is also complex as there is considerable heterogeneity in Australian livestock production systems, market systems, geography and climate (Animal Health Australia, 2014a). Further, disease control in Australia is managed by the individual states and territories (Animal Health Australia, 2014b), so for national planning purposes, a model needs to handle jurisdictional differences in the implementation of control programs. AusSpread is a spatially-explicit, farm-based state-transition microsimulation developed by the Australian Department of Agriculture and Water Resources to study FMD (Garner and Beckett, 2005). It is based on the MapBasic/MapInfo geographic information system (GIS) platform (Pitney Bowes, 2015). Runtime constraints limit AusSpread's practical use to studying disease at a regional level.

The Australian Animal DISease (AADIS) model is a national-scale epidemiological model developed by the Australian Department of Agriculture and Water Resources (Bradhurst et al., 2013, Bradhurst et al., 2015). The AADIS model is written in Java (Oracle, 2015), and employs open-source products such as OpenMap (BBN, 2015), PostgreSQL (PostgreSQL, 2015) and SQL Power Architect (SQL Power Group, 2015). A national-scale epidemiological model must be computationally efficient while addressing the needs of disease managers in terms of capturing the disease epidemiology, regional variability in transmission (for example, due to different livestock movement patterns, production systems and climates), and jurisdictional approaches to control. In this paper we present the key design features that allow the AADIS model to run complex national-scale simulations efficiently on a personal computer: a hybrid agent-based model (ABM) architecture that embeds EBMs inside herd agents; an asynchronous software architecture that features lightweight agents in an active concurrent environment; and grid-based spatial indexing. We describe the performance gains achieved through the use of uniform grid-based spatial indexing instead of R-Tree-over-GiST spatial indexing provided in the PostGIS (OSGeo, 2015) extension to PostgreSQL. We also compare the runtime performance of the AADIS ABM with the AusSpread microsimulation and discuss some advantages and disadvantages of concurrent processing over the sequential approach taken by many microsimulations such as AusSpread.

Section snippets

Hybrid model architecture

The main Australian industries vulnerable to an FMD outbreak are beef, dairy, wool, sheep meat, and pigs. This implies an FMD-susceptible national population in excess of 100 million animals (Australian Bureau of Statistics, 2014). It is possible to derive realistic individual-based contact networks from identification and tracing systems such as the Australian National Livestock Identification System (Meat and Livestock Australia, 2014). Australian cattle, for example, undergo mandatory

Spatial indexing comparison

Fig. 5 illustrates that the mean response time of spatial queries in the absence of spatial indexing was O(n), i.e., linearly dependent on the size n of the population. This is because each spatial query triggered a sequential scan over all herd records. Fig. 5 also shows how R-Tree-over-GiST spatial indexing improved the mean response time of spatial queries to O(log n). Fig. 6 illustrates how the AADIS ABM grid-based spatial indexing scheme provided approximately an eight-fold improvement in

Concurrent vs. sequential processing

As the AADIS ABM components operate concurrently, the execution time of a simulation day is effectively limited by the longest time taken by any one component. The AADIS ABM concurrent approach takes advantage of the inexpensive parallelism available on a multi-core hardware platform. Concurrency also reflects the epidemiological reality that spread and control proceed independently and in parallel during an outbreak. In contrast, the constituent tasks of a simulation day in the AusSpread

Conclusions

ABMs have a natural affinity for capturing population heterogeneity, stochasticity, spatial relationships, social systems and policy elements. An example of a field where an agent-based approach works well is animal health policy development and disease planning. The ability to incorporate livestock population heterogeneity, regional variation, jurisdiction-dependent control policies, logistics and socio-political aspects into decision support tools, brings realism to the study of complex

Acknowledgements

The AADIS ABM is a joint research venture between the Australian Department of Agriculture and Water Resources and the University of New England (UNE). The authors acknowledge both organisations for their support of the project. The authors would also like to thank Professor A.S.M. Sajeev who was a strong supporter of the project whilst at UNE. This work is funded under the Australian Government's Animal Biosecurity Response and Reform Program.

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