09:00 to 10:00 Uses and abuses of stochastic models in veterinary epidemiologyChair: D Clancy Equine influenza causes disease that, while similar to human infection caused by Influenza A H1N1 and H3N2, at least in terms of the pathogenesis, transmission and population level phylogeny, is markedly different in terms of seasonality in that there are no obvious consistent winter peaks of transmission. The talk will focus around a programme of work directed at better understanding of the epidemiology and control of equine influenza infection. The programme has used stochastic versions of SEIR models, parameterised from experimental and epidemiological data of the disease in the natural host. Optimising the use of vaccination is of particular interest. Empirical data have allowed the extension of the basic models into those assessing the impact of virus selection (antigenic drift) and explain how rather small differences observed experimentally scale up to substantial population level effects. More recent developments of explore the extension of a basic model into a one involved variably connected patches. Practical issues which face all those working in similar fields relating to parameterisation of more complex stochastic epidemiological models will be discussed and comparison will be made with other epidemiological work. INI 1 10:00 to 11:00 Bayesian inference for structured population models given final outcome dataChair: D Clancy We consider the problem of Bayesian inference for infection rates in a multi-type stochastic epidemic model in which the population has a given structure, given data on final outcome. For such data, a likelihood is both analytically and numerically intractable. This problem can be overcome by imputation of suitable latent variables. We describe two such approaches based on different representations of the epidemic model. We also consider extentions to the methodology for the situation where the observed data are a fraction of the entire population. The methods are illustrated with data on influenza outbreaks. INI 1 11:00 to 11:30 Coffee 11:30 to 12:30 Climate-driven spatial dynamics of plague among prairie dog coloniesChair: D Clancy I will present a Bayesian hierarchical model for the joint spatial dynamics of a host-parasite system. The model was fitted to long-term data on the regional plague dynamics and metapopulation dynamics of the black-tailed prairie dog, a declining keystone of North American prairies. The rate of plague transmission between colonies increases with increasing precipitation while the rate of infection from unknown sources decreases in response to hot weather. The annual dispersal distance of plague is about 10 km and topographic relief reduces the transmission rate. Larger colonies are more likely to become infected, but colony area does not affect the infectiousness of colonies. The results suggests that prairie dog movements do not drive the spread of plague through the landscape. Instead, prairie dogs are useful sentinels of plague epizootics. Simulations suggest that the model can be used for predicting long-term colony and plague dynamics as well as for identifying which colonies are most likely to become infected in a specific year. INI 1 12:30 to 13:30 Lunch at Churchill College 14:00 to 15:15 Statistical inference for epidemics among a population of householdsChair: E Renshaw This talk is concerned with a stochastic model for the spread of an SIR (susceptible $\to$ infective $\to$ removed) epidemic among a closed, finite population that contains several types of individual and is partitioned into households. A pseudolikelihood framework is presented for making statistical inference about the parameters governing such epidemics from final outcome data, when possibly only some of the households in the population are observed. The framework includes parameter estimation, hypothesis tests and goodness-of-fit. Asymptotic properties of the procedures are derived when the number of households in both the sample and the population are large, which correctly account for dependencies between households. The methodology is illustrated by applications to data on a \emph{variola minor} outbreak in Sao Paulo and to data on influenza outbreaks in Tecumseh, Michigan. INI 1 15:15 to 15:45 Tea 15:45 to 17:00 Exact Bayesian inference and model selection for some infection modelsChair: E Renshaw While much progress in the analysis of infectious disease data depends upon MCMC methodology, the simpler and more exact method of rejection sampling can sometimes be very useful. Using examples of influenza data from a population divided into households, this talk will illustrate the use of rejection sampling in model fitting; use of an initial sample to improve the efficiency of the algorithm; selection between competing models of differing dimensionality. INI 1