The construction and analysis of epidemic trees with reference to the 2001 UK foot-and-mouth outbreak

The case-reproduction ratio for the spread of an infectious disease is a critically important concept for understanding dynamics of epidemics and for evaluating impact of control measures on spread of infection. Reliable estimation of this ratio is a problem central to epidemiology and is most often accomplished by fitting dynamic models to data and estimating combinations of parameters that equate to the case-reproduction ratio. Here, we develop a novel parameter-free method that permits direct estimation of the history of transmission events recoverable from detailed observation of a particular epidemic. From these reconstructed 'epidemic trees', case-reproduction ratios can be estimated directly. We develop a bootstrap algorithm that generates percentile intervals for these estimates that shows the procedure to be both precise and robust to possible uncertainties in the historical reconstruction. Identifying and 'pruning' branches from these trees whose occurrence might have been prevented by implementation of more stringent control measures permits estimation of the possible efficacy of these alternative measures. Examination of the cladistic structure of these trees as a function of the distance of each case from its infection source reveals useful insights about the relationship between long-distance transmission events and epidemic size. We demonstrate the utility of these methods by applying them to data from the 2001 foot-and-mouth disease outbreak in the UK.