1. Contact patterns between herds: methods and visions (some results) Uno Wennergren (Tom Lindström) Linköping University Sweden

2. Inference from animal movement databases ‘Complete’ animal movement databases – All EU states – Australia, New Zeeland US – Construction of partial database From a disease spread perspective (prevention intervention) – Contact tracing – Analysis for disease spread – Prediction models, test of interventions – Commonly network analysis

3. Spatial distribution of premises Contact between premises A B CD E F G

4. A probabilistic approach What is the probability of animal movement contacts given herd and between herd characteristics? Bayesian analysis – Markov Chain Monte Carlo In the data base – Location – Herd size – Production type (pigs only)

5. MCMC Bayesian Cutting edge statistics 5 Values for a and b at step t Calculate likelihood of data under a, b and a’, b’ as Propose a’ and b’ for step t+1 If P(d|a’,b’) > P(d|a,b) accept a’,b’ a(t+1) = a’, b(t+1) = b’ If P(d|a’,b’) < P(d|a,b) accept a’,b’ with probability P(d|a’,b’)/P(d|a,b) If accept, a(t+1) = a’, b(t+1) = b’ If reject, a(t+1) = a, b(t+1) = b Database

6. Agenda Distance dependence Production types Combining everything Does it matter? Visions

7. Distance Probability as a function of distance Scale and shape Production type The probability of transport t from a herd of type I to type J

8. Production type Pig holdings only Sow Pool Center Satellites Breeding pyramid Sow pool Farrow-to- finish

9. Production type TO FROM Sow pool center Sow pool satellite Farrow-to-finish Nucleus herd Piglet producer Multiplying herd Fattening herd Missing information Sow pool center 77 (63,94) 120 (110,140) 0.79 (0.41,1.3) 0.59 (0.014,2.2) 4.0 (3.3,4.7) 6.1 (3.3,9.9) 10 (9.2,12) 13 (11,16) Sow pool satellite 120 (110,130) 1.6 (1.1,2.1) 0.033 (0.001,0.095) 0.11 (0.003,0.43) 0.015 (0.002,0.038) 0.11 (0.002,0.34) 9.3 (8.6,10) 0.51 (0.24,0.84) Farrow-to- finish 2.4 (1.7,3.1) 0.047 (0.002,0.13) 0.35 (0.28,0.43) 0.037 (0.001,0.14) 0.12 (0.087,0.15) 0.42 (0.22,0.67) 1.8 (1.6,2.0) 2.3 (2.0,2.5) Nucleus herd 69 (56,82) 0.51 (0.11,1.2) 12 (10,13) 130 (120,150) 12 (11,13) 120 (100,130) 3.6 (3.0,4.3) 16 (13,18) Piglet producer 5.3 (4.5,6.2) 0.5 (0.35,0.65) 0.45 (0.39,0.52) 0.13 (0.031,0.26) 0.29 (0.25,0.33) 0.097 (0.008,0.22) 9.5 (9.0,10) 3.2 (2.9,3.5) Multiplying herd 150 (140,170) 1.3 (0.58,2.3) 20 (18,22) 0.73 (0.079,2.1) 25 (23,26) 15 (11,20) 11 (10,13) 8.8 (7.2,11) Fattening herd 0.95 (0.61,1.3) 0.019 (0.001,0.049) 0.015 (0.005,0.030) 0.076 (0.015,0.17) 0.019 (0.010,0.031) 0.39 (0.24,0.58) 0.18 (0.15,0.22) 0.17 (0.11,0.24) Missing information 2.1 (1.3,3.2) 0.11 (0.018,0.22) 0.16 (0.095,0.24) 0.53 (0.19,1.0) 0.066 (0.034,0.10) 0.14 (0.007,0.38) 0.97 (0.82,1.1) 0.84 (0.60,1.1) Lindström et al. 2010. Prev. Vet. Med. 95

10. Distance Bars: Observed movement distances; Dotted line: Spatial kernel (Simpler model); Solid line: Spatial kernel + uniform part (Mixture model) CattlePigs Lindström et al. 2009. Prev. Vet. Med. 91

11. Distance Known as – Generalized normal distribution – Power exponential distribution P: contact probability d: distance a,b: regulates shape and scale S: normalizing of the distribution

12. Distance Is this function sufficient to model distance dependence in contact probability? Comparison of two models –M1:–M1: –M2:–M2: Compared by their posterior distribution

13. Agenda Distance dependence Production types Combining everything Does it matter? Visions

14. Production type More than one type per holding Estimates of v Lindström et al. 2010. Prev. Vet. Med. 95

15. Production type The probability of transport t from a herd of type I to type J

16. Simulation Sow Pool Center Satellites Farrow-to- finish Lindström et al. 2010. Prev. Vet. Med. 95 Production type

17. Agenda Distance dependence Production types Combining everything Does it matter? Visions

18. Combining everything… Distance, production type, herd size – Pigs only Herd size – Reported for sows and fattening pigs separately – Probability of ingoing/outgoing transports – Modeled as a power law relationship

19. Combining everything… Lindström et al. Prev. Vet. Med. In press

20. Combining everything… Hierarchical priors for distance parameters D1D1 D2D2 D3D3 DnDn θ1θ1 θ2θ2 θ3θ3 θnθn ξ

21. Combining everything… Heterogeneous contact structure Contact probability depends on production types The influence of herd size on contact probability varies between production type and demography (sows and fattening pigs)

22. Combining everything… Sow pool center Sow pool satellite Farrow- to-finish Nucleus herd Piglet producer Multiplying herd Fattening herd Missing information Outgoing Fattening pigs 0.043-0.035-0.0330.18-0.00490.0210.36-0.44 Outgoing Sows 0.310.240.670.690.470.440.68-0.29 Incoming Fattening pigs 0.0290.091-0.03410.045-0.0130.51-1.2 Incoming Sows 0.370.150.52-0.860.660.260.120.15 Lindström et al. Prev. Vet. Med. In press

23. Combining everything… Distance dependence differs between production types Green: Sow pool centers to satellites Blue: Nucleus to Multiplying herds Red: Farrow-to-finish to Fattening herds

24. Combining everything… Good fit with observed distances Distance Proportion of movements

25. Combining everything… Simulation – GLM Lindström et al. Prev. Vet. Med. In press

26. Agenda Distance dependence Production types Combining everything Does it matter? Visions

27. Influence on disease spread dynamics Effect of production type, herd size and between herd distance. Simulate disease spread with reduced models 1.Mass action mixing 2.Full model 3.No production type structure 4.No herd size effect 5.No distance dependence 6.No production type difference in distance dependence

28. Influence on disease spread dynamics Mean nr of infected vs. time Lindström et al. Forthcoming

29. Influence on disease spread dynamics Final epidemic size Lindström et al. Forthcoming

30. Influence on disease spread dynamics Conclusion: – Production type differences in contact probability has the highest impact on disease spread dynamics – Herd size and distance dependence is also important

31. Effect of kernel shape Effect of scale is obvious How about the kernel shape? Does the effect of the shape depend on the spatial arrangement of farms? Description of the point pattern distribution – Spectral representation

32. Spectral representation Commonly used in time series analysis Set of sine elements Extension to two dimensions

33. Spectral representation …and for point patterns – Mugglestone and Renshaw 2001, Environ. Ecol. Stat. Two measures – Lindström et al, Proc. Roy. Soc. Lond. B. In press. – Continuity Spatial autocorrelation – Contrast Difference in density

34. Spectral representation Contrast: 4.9 Continuity: 2.0 Contrast: 2.2 Continuity: 1.8 Contrast: 1.5 Continuity: 1.1 Contrast: 4.2 Continuity: 1.0 – Continuity Spatial autocorrelation – Contrast Difference in density

35. Effect of kernel shape Simulation with different scale and shape – Distance – Nr infected Lindström et al, Proc. Roy. Soc. Lond. B. In press.

36. Effect of kernel shape How to implement distance dependence of infection probability? – Absolute or Relative Contrast Continuity Piglet producers to Fattening herds

37. Agenda Distance dependence Production types Combining everything Does it matter? Visions

38. Data lots or less Lots of it – be sure that the sample(s) of yesterday predict today's/tomorrows pattern Less of it – – Be sure that the sample(s) represent the pattern of yesterday – ………………….. predict today's/tomorrows pattern Transport routes – database only on farm and slaughterhouse (no stops) Part of data on contacts - transports in US

39. Partial data on all contacts Will the data reveal the network (of yesterday)? a)network metrics of the sample, will it represent the metrics of the complete dataset? b)Will a simulation of disease spread based on the data represent a simulation based on the complete dataset (all transports)?

40. Partial data on all contacts A.network metrics of the sample, will it represent the metrics of the complete dataset? B.Will a simulation of disease spread based on the data represent a simulation based on the complete dataset? Is A a necessary condition of B? Is it a sufficient condition of B?

41. Is A a necessary and sufficient condition of B? Only if high correlation between disease spread and network metrics. Is this true for more complicated networks: spatial patterns and kernels?

42. Is A a necessary and sufficient condition of B? Under what conditions* will a metric correlate with a specific feature of spread of disease How much data is needed to asses the metric, under given conditions? (fulfill A) * Condition is spatial pattern and kernel

43. A given condition: – Spatial pattern(s) and kernel(s) If at 5% of all possible links the spread of disease has converged to a stationary rate (don’t incease with more links, weighted ones) - network metrics should also converge at this point. Relates to a fully connected network

44. Condition: random pattern – exponential kernel Around 4%: the mean number of infected holdings has converged, fully connected Around 2%: the mean number of infected holdings has converged on shorter time scales, not fully connected assortativity Clustering coefficient Lennartsson et al. manuscript Link density Not the best set of links? Other conditions? Adding links – more data?

45. Other conditions spatial patterns - kernels Not studied yet- need methods to generate the conditions the spatial patterns (patially solved) the spatial kernels (solved) networks metrics that spans the empirically found intervals

46. Network algorithm Spec Net 1 (spectral method) Generated networks with different values for the parameters γ, σ, κ, n and link density: Ref: Håkansson et al (2010). Advances in Complex Systems. Connect to data- kernels and spatial patterns

47. Adding focal nodes Spec Net 2 To be able to generate a broader spectrum of network structures. Focal nodes: 10 times higher probability for connection between a focal node and a regular node. Support by importance of production type. CM algorithm Non-spatial distribution of nodes Given degree distribution Given level of clustering Build triangles between nodes

48. Preliminary results: range of network measures

49. Less data - Need to generate networks with known characteristics – If related to spatial patterns – measure patterns of the nodes/holdings Probably need layers of spatial patterns – focal and regular nodes. Indicated by importance of production type. – also relates to slaughterhouses – If related to spatial kernels – measure kernels between nodes/holdings Probably need different kernels of and between layers (production types)

50. Less data – the route of a truck Contact between holdings due to animal transport routes, for example picking up animals from different holdings on its way to the slaugtherhouse. We’ve made som algorthims to test different routeplanning. It turns out very different depending on planning tools and aims. – Reduce transport distance by 30-40% – Another 30% if reallocate between slaughterhouses yet same capacity at each slaughterhouse

51. Summing up Lots of data- – Describe todays pattern – Predict today by yesterdays data MCMC Bayesian sort out importance, distance production types etc PPL – analyse and generate spatial pattern (point patterns) Less data – – Need to figure out how it depend on conditions Spatial patterns Kernels Layers Network algorithms: Spec Net connects empirically patterns with generated ones