1. Brief Description of the DEFRA E. coli O157 project Post-doc: Joanne Turner DEFRA Fellow: Nigel French P. I.’s: Roger Bowers, Mike Begon

2. Aims of the DEFRA E. coli O157 Project To develop deterministic and stochastic models of pathogen transmission –transmission within and between 4 animal management groups –both direct and via infectious units in environment –parameterised for E.coli O157 within a typical UK dairy herd. To suggest ways of reducing the prevalence of food-borne pathogens on typical UK dairy farms –by identifying key model parameters. To assist the evaluation of control methods at the human consumption level by contributing stochastic modelling results to the Quantitative Microbial Risk Assessment –by providing distributions of prevalence in the lactating group before and after various hypothetical interventions have been applied.

3. Diagram of Transmission within a Dairy Herd Parameter associated with each arrow (39 parameters in total) maturation dry/lactating cycle recovery culling shedding transmission replacement host death pooling pathogen death

4. Dynamic Equations for Lactating Group dry/lactating cycle transmission sheddingdeath of pathogen

5. Plots of R 0 full model without intervention full model with intervention DD LL 1.0 LL DD direct and within-group indirect transmission model without intervention direct and within-group indirect transmission model with intervention

6. Stochastic model (at t=150 days) Output from the Stochastic Model 1 parameter set, 100 simulations, (effect of intervention) average prevalence each final size 100 parameter sets, average of 100 simulations for each parameter set, (between-herd variation)

7. Lactating group Weaned group deterministic model stochastic model zWzW WW WW qWqW UU pDpD parameters description symbol recovery shedding indirect trans. path. death recovery shedding indirect trans. path. death direct trans. recovery pooling LL LL zLzL qLqL LL -0.8151 0.7532 0.4404 -0.3402 -0.6818 0.3245 -0.3558 0.7695 0.4301 -0.3289 -0.6544 0.3931 0.3887 0.4046 -0.5863 0.4069 -0.3367 -0.8045 0.4005 -0.5808 0.3660 Sensitivity Analysis of Herd Prevalence Use partial rank correlation coefficients (PRCCs) to identify parameters that greatly affect herd prevalence.

8. Problem with Parameterisation Aim was to identify feasible values for each parameter by reviewing experimental studies designed to examine individual parts of the process. Transmission experiments are not possible for E. coli O157 (no clinical symptoms, no protective immune response). So, we cannot directly estimate the transmission parameters. Crude method: We used the mean values of the other model parameters, then adjusted the direct and indirect transmission parameters so that the prevalence in each group (given by the deterministic model) matched the mean prevalence in each group from the DEFRA longitudinal study. The direct and indirect transmission parameters were such that approx 50% of transmission in each group was direct. How can we estimate the transmission parameters from prevalence data? (MCMC approach not possible with data available.)

9. Problem with Large Stochastic Models Some algebraic results are available for the 4-group deterministic model (e.g. plots of R 0 ). Only numerical results are available for the 4-group stochastic model. How can we thoroughly investigate feasible parameter space when the model has 39 parameters? What is the best way to summarise numerical results?