Improving the computational efficiency of an agent-based spatiotemporal model of livestock disease spread and control
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.
References (63)
- et al.
Modeling the spatial spread of infectious diseases: the global epidemic and mobility computational model
J. Comput. Sci.
(2010) - et al.
Daniel Bernoulli's epidemiological model revisited
Math. Biosci.
(2002) - et al.
Simulating the spatial dynamics of foot and mouth disease outbreaks in feral pigs and livestock in Queensland, Australia, using a susceptible-infected-recovered cellular automata model
Prev. Veterinary Med.
(2005) - et al.
Further towards a taxonomy of agent-based simulation models in environmental management
Math. Comput. Simul.
(2004) - et al.
Supporting frequent updates in R-Trees: a bottom-up approach
- et al.
A comparative analysis of parallel processing and super-individual methods for improving the computational performance of a large individual-based model
Ecol. Model.
(2008) - et al.
How do resources influence control measures during a simulated outbreak of foot and mouth disease in Australia?
Prev. Veterinary Med.
(2014) - et al.
Applying GIS and high performance agent-based simulation for managing an old world screwworm fly invasion of Australia
Acta Trop.
(2014) Agricultural Commodities, Australia
(2014)Animal Health in Australia 2013
(2014)
Disease Strategy: Foot-and-mouth Disease (Version 3.4)
When individual behaviour matters: homogeneous and network models in epidemiology
J. R. Soc. Interface
Description of an epidemic simulation model for use in evaluating strategies to control an outbreak of foot-and-mouth disease
Am. J. Veterinarian Res.
OpenMap. BBN Technologies
Developing multi-agent systems with a FIPA-compliant agent framework
Softw. Pract. Exp.
Modelling the spread of livestock disease on a national scale: the case for a hybrid approach
A hybrid modelling approach to simulating foot-and-mouth disease outbreaks in Australian livestock
Front. Environ. Sci.
Potential Socio-economic Impacts of an Outbreak of Foot-and-mouth Disease in Australia
Pattern-oriented Software Architecture – a System of Patterns
BioWar: scalable agent-based model of bioattacks
IEEE Trans. Syst. Man Cybern. Part A Syst. Humans
The importance of including intra-herd transmission in a foot-and-mouth disease model
A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides
ACM Trans. Math. Softw.
Blackboard systems
AI Expert
Introduction to agent-based modelling
Multi agent simulation: beyond social simulation. multi-agent-based simulation
Lect. Notes Comput. Sci.
Neighbour lists in smoothed particle hydrodynamics
Int. J. Numer. Methods Fluids
Determining the Number of Iterations for Monte Carlo Simulations of Weapon Effectiveness (No. NPS-MAE-04-005)
Data-parallel algorithms for agent-based model simulation of tuberculosis on graphics processing units
Quad trees: a data structure for retrieval on composite keys
Acta Inform.
Modelling the spread of foot-and-mouth disease in Australia
Aust. Veterinary J.
Evaluating alternative approaches to managing animal disease outbreaks – the role of modelling in policy formulation
Veterinaria Ital.
Cited by (25)
Comparing surveillance approaches to support regaining free status after a foot-and-mouth disease outbreak
2021, Preventive Veterinary MedicineCitation Excerpt :The effectiveness and the cost of baseline surveillance approaches, based on the European FMD directive (EU, 2003) were compared with alternative approaches in which the sampling regime, sampling approaches and/or the diagnostic tests used were varied. The AADIS model (Bradhurst et al., 2015, 2016) is a national-scale epidemiological model used by animal health authorities in Australia to support FMD planning and preparedness. It is a spatiotemporal agent-based simulation of the spread and control of an emergency animal disease.
A generalised and scalable framework for modelling incursions, surveillance and control of plant and environmental pests
2021, Environmental Modelling and SoftwareCitation Excerpt :The APPDIS and AADIS modelling frameworks have a common underlying software baseline (Bradhurst, 2015). APPDIS thus inherits from previous AADIS verification and validation activities, and modelling studies (Bradhurst, 2015; Bradhurst et al., 2015; Bradhurst et al., 2016; Garner et al., 2016; Bradhurst et al., 2019; Firestone et al., 2019; Bradhurst et al., 2021; Firestone et al., 2020). APPDIS models were instantiated for Anoplolepis gracilipes (yellow crazy ant) and Bactrocera dorsalis (Oriental fruit fly) case studies during development of the framework.
Replicating complex agent based models, a formidable task
2017, Environmental Modelling and SoftwareCitation Excerpt :Agent based models (ABM) are widespread throughout the biological, ecological and environmental sciences (Bithell and Brasington, 2009; Bradhurst et al., 2016; Grimm, 1999; Grimm et al., 2005; Matthews et al., 2007).
Simple or complicated agent-based models? A complicated issue
2016, Environmental Modelling and SoftwareCitation Excerpt :Computational constraints: Beyond issues of data availability, resource considerations for implementation and analysis may play a (practical) role in deciding how to structure the model. Among these resource consideration, computational demands can pose problems for ABM modellers due to, for example, the large individual population and detailed representation of their behaviours (Bradhurst et al., 2016). For example, with the aim of being able to simulate land-use change over large extents (e.g., the entire European Union) the CRAFTY ABM framework needed to make seems unrealistic assumptions on agent behaviours to ensure computational efficiency was adequate for the purpose (Murray-Rust et al., 2014).
Surrogate modelling of a detailed farm-level model using deep learning
2024, Journal of Agricultural Economics