Spatial survival analysis of infectious animal diseases
This thesis investigates the feasibility of using spatial survival modelling techniques to develop dynamic space-time predictive models of risk for infectious animal disease epidemics. Examples of diseases with potentially vast socioeconomic impacts include avian influenza, bovine tuberculosis and foot-and-mouth disease (FMD), all of which have received wide coverage in the recent media. The relatively sporadic occurrence of such large scale animal disease outbreaks makes determination of optimal control policies difficult, and policy makers must balance the relative impacts of different response strategies based on little prior information. It is in this situation that the use of mathematical and statistical modelling techniques can provide powerful insights into the future course of an infectious epidemic. The motivating example for this thesis is the outbreak of FMD in Devon in 2001, however we are interested in developing more general techniques that can be applied to other animal diseases. Many of the models fitted to the 2001 UK FMD data set have focussed on modelling the global spread of the disease across the entire country and then using these models to assess the effects of nationwide response strategies. However it has been shown that the dynamics of the disease are not uniform across the whole of the UK and can vary significantly across different spatial regions. Of interest here is exploring whether modelling at a smaller spatial scale can provide more useful measures of risk and guide the development of more efficient control policies. We begin by introducing some of the main epidemiological issues and concepts involved in modelling infectious animal diseases, from the microscopic through to the farm population level. We then discuss the various mathematical modelling techniques that have applied previously and how they relate to various biological principals discussed in the earlier chapters. We then highlight some limitations with these approaches and offer potential ways in which survival analysis techniques could be used to overcome some of these problems. To this end we formulate a spatial survival model and fit it to the Devon data set with some naive initial covariates that fail to capture the dynamics of the disease. Some work by colleagues at the Veterinary Laboratories Agency, Weybridge (Arnold 2005), produced estimates of viral excretion rates for infected herds of different species type over time, and these form the basis for the development of a dynamic space-time varying viral load covariate that quantifies the viral load acting at any spatial location at any point in time. The novel use of this covariate as a means of censoring the data set via exposure is then introduced, though the models still fail to explain the variation in the epidemic process. Two potential reasons for this are identified - the possible presence of non-localised infections and/or premise varying susceptibility. We then explore ways in which the survival approach can be extended to model more than one epidemic process through the use of mixture and long-term survivor models. Some simple simulations suggest that resistance to infection is the most likely cause of the poor model fits, and a series of more complex simulation experiments show that both the mixture and long-term survivor models offer various advantages over the conventional approach when resistance is present in the data set. However key to their performance is the ability to correctly capture the mixing, although in the worst case scenario they still replicate the results from the conventional model. We also use these simulations to explore potential ways in which space-time predictions of the hazard of infection can be used as a means of targeting control policies to areas of ‘high-risk’ of infection. This shows the importance of ensuring that the scale of the control order matches the scale of the epidemic, and suggests possible dangers when using global level models to derive response strategies for situations where the dynamics of the disease change at smaller spatial scales. Finally we apply these techniques to the Devon data set and offer some conclusions and future work.