Modelling the spread of livestock disease on a national scale: the case for a hybrid approach

Abstract

An epidemic of exotic disease in a livestock population can lead to substantial economic losses. For example, the projected cost of a foot-and-mouth disease (FMD) epidemic in Australia is in the billions of dollars. This includes the direct cost of eradicating the disease (e.g., movement restrictions, culling and vaccination), and the impact to export markets from the loss of Australia's FMD-free status. Epidemics can be difficult to study empirically, particularly if a pathogen is dangerous, rare, or simply not present in a country. In these circumstances a model of disease spread can be a valuable epidemiological tool. When responding to an epidemic, animal health personnel might be restricted to enacting existing policies that leave little scope for the trialing of new control strategies. Computational modelling compensates for the limited opportunities an epidemiologist has to experiment in the field. Models of disease spread typically employ population-level approaches such as equation-based modelling, or individual-level approaches such as agent-based modelling. Population-level models can be concise and computationally efficient, but they do not isolate individual contributions to an epidemic. The finer granularity of individual-level models can introduce a computational overhead. In the case of a very largescale model, an individual-level approach can require a highly parallel platform such as a high-performance computing cluster in order to function efficiently. Epidemics are dynamically shaped by the complex interplay between host, pathogen and the environment. Modelling livestock disease spread on a national scale presents unique challenges due to large populations, varying herd types and farming practices, and regional and geopolitical differences. An alternative to pure population-level and individual-level modelling is a fusion of the two approaches into a hybrid model. This tactic is employed in the Australian Animal Disease Spread (AADIS) model, currently under development. The spread of disease within a herd is modelled from the top down by a system of ordinary differential equations. The spread of disease between herds is modelled from the bottom up by a spatially-aware agentbased model. Homogeneity is a reasonable abstraction for a herd of domestic animals and thus intra-herd spread of disease is well suited to equation-based modelling. The national set of herds is however, heterogeneous, making inter-herd spread of disease well suited to agent-based modelling. AADIS models the transfer of disease from an infectious herd to a susceptible herd by five stochastic spread pathways: direct contact, indirect contact, local spread, airborne transmission and spread through saleyards. Herds can be viewed abstractly as autonomous nodes in a network. Over discrete time steps of one day, the disease spread pathways generate the network topology. Network paths can subsequently be traversed forward to assess the downstream impact of an infected herd, or backward to trace the historical infection route. The network topology thus captures the spatiotemporal history of the simulated epidemic. AADIS is implemented in Java and employs open-source products such as PostgreSQL, PostGIS and OpenMap. It has an asynchronous object-oriented architecture that takes advantage of the inexpensive parallelism available on a multi-core x64 target.