| Summary: | This thesis comprises a number of inter-related parts. For most of the thesis we are concerned with developing a new statistical technique that can enable the identi cation of the optimal control by comparing competing control strategies for stochastic epidemic models in real time. In the second part, we develop a novel approach for modelling the spread of Peste des Petits Ruminants (PPR) virus within a given country and the risk of introduction to other countries. The control of highly infectious diseases of agriculture crops, animal and human diseases is considered as one of the key challenges in epidemiological and ecological modelling. Previous methods for analysis of epidemics, in which different controls are compared, do not make full use of the trajectory of the epidemic. Most methods use the information provided by the model parameters which may consider partial information on the epidemic trajectory, so for example the same control strategy may lead to different outcomes when the experiment is repeated. Also, by using partial information it is observed that it might need more simulated realisations when comparing two different controls. We introduce a statistical technique that makes full use of the available information in estimating the effect of competing control strategies on real-time epidemic outbreaks. The key to this approach lies in identifying a suitable mechanism to couple epidemics, which could be unaffected by controls. To that end, we use the Sellke construction as a latent process to link epidemics with different control strategies. The method is initially applied on non-spatial processes including SIR and SIS models assuming that there are no observation data available before moving on to more complex models that explicitly represent the spatial nature of the epidemic spread. In the latter case, the analysis is conditioned on some observed data and inference on the model parameters is performed in Bayesian framework using the Markov Chain Monte Carlo (MCMC) techniques coupled with the data augmentation methods. The methodology is applied on various simulated data sets and to citrus canker data from Florida. Results suggest that the approach leads to highly positively correlated outcomes of different controls, thus reducing the variability between the effect of different control strategies, hence providing a more efficient estimator of their expected differences. Therefore, a reduction of the number of realisations required to compare competing strategies in term of their expected outcomes is obtained. The main purpose of the final part of this thesis is to develop a novel approach to modelling the speed of Pest des Petits Ruminants (PPR) within a given country and to understand the risk of subsequent spread to other countries. We are interested in constructing models that can be fitted using information on the occurrence of outbreaks as the information on the susceptible population is not available, and use these models to estimate the speed of spatial spread of the virus. However, there was little prior modelling on which the models developed here could be built. We start by first establishing a spatio-temporal stochastic formulation for the spread of PPR. This modelling is then used to estimate spatial transmission and speed of spread. To account for uncertainty on the lack of information on the susceptible population, we apply ideas from Bayesian modelling and data augmentation by treating the transmission network as a missing quantity. Lastly, we establish a network model to address questions regarding the risk of spread in the large-scale network of countries and introduce the notion of ` first-passage time' using techniques from graph theory and operational research such as the Bellman-Ford algorithm. The methodology is first applied to PPR data from Tunisia and on simulated data. We also use simulated models to investigate the dynamics of spread through a network of countries.
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