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Transmission network modelling to infer ‘who infected whom’ in infectious disease outbreaks is a highly active area of research. Outbreaks of foot-and-mouth disease have been a key focus of transmission network models that integrate genomic and epidemiological data. The aim of this study was to extend Lau’s systematic Bayesian inference framework to incorporate additional parameters representing predominant species and numbers of animals held on a farm. Lau’s Bayesian Markov chain Monte Carlo algorithm was reformulated, verified and pseudo-validated on 100 simulated outbreaks populated with demographic data Japan and Australia. The modified model was then implemented on genomic and epidemiological data from the 2010 outbreak of foot-and-mouth disease in Japan, and outputs compared to those from the SCOTTI model implemented in BEAST2. The modified model achieved improvements in overall accuracy when tested on the simulated outbreaks. When implemented on the actual outbreak data from Japan, infected farms that held predominantly pigs were estimated to have five times the transmissibility of infected cattle farms and be 49% less susceptible. The farm-level incubation period was 1 day shorter than the latent period, the timing of the seeding of the outbreak in Japan was inferred, as were key linkages between clusters and features of farms involved in widespread dissemination of this outbreak. To improve accessibility the modified model has been implemented as the R package ‘BORIS’ for use in future outbreaks.

This Research Topic presents valuable studies presenting different aspects and implementations of mathematical modeling for disease spread and control in the veterinary field.

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.

Disease managers face many challenges when deciding on the most effective control strategy to manage an outbreak of foot-and-mouth disease (FMD). Decisions have to be made under conditions of uncertainty and where the situation is continually evolving. In addition, resources for control are often limited. A modeling study was carried out to identify characteristics measurable during the early phase of a FMD outbreak that might be useful as predictors of the total number of infected places, outbreak duration, and the total area under control (AUC). The study involved two modeling platforms in two countries (Australia and New Zealand) and encompassed a large number of incursion scenarios. Linear regression, classification and regression tree, and boosted regression tree analyses were used to quantify the predictive value of a set of parameters on three outcome variables of interest: the total number of infected places, outbreak duration, and the total AUC. The number of infected premises (IPs), number of pending culls, AUC, estimated dissemination ratio, and cattle density around the index herd at days 7, 14, and 21 following first detection were associated with each of the outcome variables. Regression models for the size of the AUC had the highest predictive value (R2 = 0.51-0.9) followed by the number of IPs (R2 = 0.3-0.75) and outbreak duration (R2 = 0.28-0.57). Predictability improved at later time points in the outbreak. Predictive regression models using various cut-points at day 14 to define small and large outbreaks had positive predictive values of 0.85-0.98 and negative predictive values of 0.52-0.91, with 79-97% of outbreaks correctly classified. On the strict assumption that each of the simulation models used in this study provide a realistic indication of the spread of FMD in animal populations. Our conclusion is that relatively simple metrics available early in a control program can be used to indicate the likely magnitude of an FMD outbreak under Austr

Foot-and-mouth disease (FMD) is a highly contagious and economically important viral disease of cloven-hoofed animals. Australia's freedom from FMD underpins a valuable trade in live animals and animal products. An outbreak of FMD would result in the loss of export markets and cause severe disruption to domestic markets. The prevention of, and contingency planning for, FMD are of key importance to government, industry, producers and the community. The spread and control of FMD is complex and dynamic due to a highly contagious multi-host pathogen operating in a heterogeneous environment across multiple jurisdictions. Epidemiological modeling is increasingly being recognized as a valuable tool for investigating the spread of disease under different conditions and the effectiveness of control strategies. Models of infectious disease can be broadly classified as: population-based models that are formulated from the top-down and employ population-level relationships to describe individual-level behavior; individual-based models that are formulated from the bottom-up and aggregate individual-level behavior to reveal population-level relationships; and hybrid models which combine the two approaches into a single model. The Australian Animal Disease Spread (AADIS) hybrid model employs a deterministic equation-based model (EBM) to model within-herd spread of FMD, and a stochastic, spatially-explicit agent-based model (ABM) to model between-herd spread and control. The EBM provides concise and computationally efficient predictions of herd prevalence and clinical signs over time. The ABM captures the complex, stochastic and heterogeneous environment in which an FMD epidemic operates. The AADIS event-driven hybrid EBM/ABM architecture is a flexible, efficient and extensible framework for modeling the spread and control of disease in livestock on a national scale. We present an overview of the AADIS hybrid approach, a description of the model's epidemiological capabilities, and