Stochastic Systems Approaches to Disease Control

Recent developments in network theory have provided new avenues for studying the spread of disease within populations. However, there is a need to develop dynamic generative models of networks that can capture the dynamic nature of many real-world systems that typical models cannot account for. Models of the spread of livestock disease have frequently employed traditional network approaches, but with the availability of highly detailed animal movement datasets, there is unprecedented scope to develop generative models of livestock trade parameterised by these data and exploring the spread of disease modulated by trade. Livestock diseases incur significant financial burdens on farms and governments, and the presence of disease remains a constant issue, so developing new insights and novel control strategies is vital. Analytically tractable generative models of livestock trade, parameterised to the Scottish cattle trading system, are developed, incorporating dynamics such as time-varying trading partnerships that, to date, have not been accounted for. Expressions for the basic reproduction number R0 are obtained and manipulations to trading behaviour are shown to reduce $R_0$ while maintaining farm business requirements. Extended models, accounting for time-varying trading behaviours, are developed. Individual-based adaptation in response to changes in trading propensities is shown to mitigate the prevalence reducing potential of such changes, highlighting the need to account for behavioural responses when modelling disease spread. Typical disease control measures, such as post-movement testing and risk aversion are shown to be effective in controlling disease, but can perturb the trading system. When parameterised to the Scottish cattle trade system, the impact of these control measures on prevalence is explored. The models presented here are a first attempt at analysing trade and its effect on disease spread at a national scale for a highly heterogeneous system using a generative network modelling approach, and can be extended to other real-world systems.