Temporal modelling of disease outbreaks using state space and delay differential equations.

The two processes of outbreak identification and disease modelling are fundamental in the study of disease outbreaks affecting livestock and wildlife. Rapid detection and the implementation of appropriate preventative or control measures from an understanding of the mechanisms of disease spread may limit the impact of an outbreak. The performance of several on-line warning algorithms in their ability to detect outbreaks in both real-life and simulated data is investigated. A version of Farrington's well established outbreak detection algorithm, referred to as the EDS scheme is compared to approaches based on the Kalman Filter, namely a Prediction Interval approach and three types of CUSUM scheme. All the schemes are able to successfully identify outbreaks and we find that no single approach appears to outperform the others in all the measures considered. However the EDS scheme is the most efficient in detecting outbreaks promptly and one of the CUSUM schemes is best at producing consistent warnings throughout the outbreak period. In addition we formulate deterministic models describing the transmission dynamics of the midge-borne disease bluetongue, with cattle and sheep as hosts. The models take the form of delay differential equations and incorporate the incubation time of bluetongue in cattle, sheep and midges, and also the larval developmental time of midges. An autonomous model assuming midges to be active year round and a periodic model allowing midge activity to vary with the seasons are analysed. The transmission of the disease via midge diffusion and migration is studied in detail and the effects of vaccination are also considered. Important findings include the need for prompt diagnosis of latent infection and appropriate action before the animal becomes infectious, and the need for measures that reduce insect bites. This reinforces the importance of timely identification of disease outbreaks in order for effective intervention to be possible