where we again fix S s to be 1 to avoid model over specification. The force of infection (3) and model log likelihood equation (7) change accordingly. Assuming transmission parameters were constant in time throughout the epidemic is obviously a crude simplification. However, allowing infectivity to vary continuously in time results in an over-specified model and problems of parameter identification and confounding. We therefore examined two sets of models in which changes in transmission parameter were restricted to 2 significant points in time denoted by T cut , namely 23 rd February (when the national ban on animal movements was introduced) and 31 st March (when control measures were intensified and the so called 24/48 hour IP/CP culling policy was introduced). Models were respectively fitted to the individual case data from the start of the epidemic (conditioning on the first infection) or from after 23rd February (conditioning on the 54 farms that were already infected by that date). A detailed history of the epidemic is given by Kao [9] . We separately fitted model variants which assumed a discrete change in parameters on 23 rd February and on 31 st March. Confounding meant that only a very limited number of parameters could be varied in time, so we examined the effect of varying infectiousness and kernel parameters separately. We fitted four separate time-varying model variants: (i) varying the cattle infectivity by a factor and keeping sheep infectivity constant through time (Cattle Infectivity model); (ii) varying sheep infectivity by a factor but not cattle infectivity (Sheep Infectivity model); (iii) varying both cattle and sheep infectivity by the same ratio (Cattle & Sheep Infectivity model); (iv) varying the kernel parameters (Time Varying Kernel model). For the last model variant we also fitted a version which includes non-assortative mixing between species (see equation (8)). Hence the most general mathematical expression of the transmission model is: