Contact patterns between herds: methods and visions (some results)

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

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 • Predictionmodels, test of interventions • Commonly network analysis

Spatial distribution of premises • Contact betweenpremises E C D A G F B

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)

? ! MCMC BayesianCuttingedgestatistics Database Values for a and b at step t Propose a’ and b’ for step t+1 Calculate likelihood of data under a, b and a’, b’ as 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 reject, a(t+1) = a, b(t+1) = b If accept, a(t+1) = a’, b(t+1) = b’

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

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

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

Production type • Lindström et al. 2010. Prev. Vet. Med. 95

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

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

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

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

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

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

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

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

Combining everything… • Hierarchical priors for distance parameters ξ θ1 θ2 θ3 θn D1 D2 D3 Dn

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)

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

Combining everything… • Distance dependence differs between production types Green: Sow pool centersto satellites Blue: Nucleus toMultiplying herds Red: Farrow-to-finishto Fattening herds

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

Influence on disease spread dynamics • Effect of production type, herd size and between herd distance. • Simulate disease spread with reduced models • Mass action mixing • Full model • No production type structure • No herd size effect • No distance dependence • No production type difference in distance dependence

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

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

Effect of kernel shape • Effect of scale is obvious • How about the kernel shape? • Does the effect of the shapedepend on the spatial arrangement of farms? • Description of the point pattern distribution • Spectral representation

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

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

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

Datalots 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

Partial data on all contacts Will the data reveal the network (of yesterday)? • networkmetrics of the sample, will it represent the metrics of the complete dataset? • Will a simulation of diseasespreadbased on the data represent a simulation based on the complete dataset (all transports)?

Partial data on all contacts • network metrics of the sample, will it represent the metrics of the complete dataset? • 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?

Is A anecessary and sufficientcondition of B? Onlyif high correlationbetweendiseasespread and networkmetrics. Is this true for morecomplicatednetworks: spatial patterns and kernels?

Is A anecessary and sufficientcondition of B? Under whatconditions* will a metriccorrelate with a specific feature of spread of disease Howmuch data is needed to asses the metric, under given conditions? (fulfill A) * Condition is spatial pattern and kernel

A given condition: • Spatial pattern(s) and kernel(s) • If at 5% of all possiblelinks the spread of disease has converged to a stationary rate (don’tincease with morelinks, weightedones) - networkmetricsshouldalsoconverge at this point. Relates to a fullyconnectednetwork

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 Link density Clustering coefficient Link density Not the best set of links? Otherconditions? Addinglinks – more data? Lennartsson et al. manuscript

Otherconditionsspatial 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

Network algorithmSpec Net 1 (spectralmethod) • Generated networks with different values for the parameters γ, σ, κ, n and linkdensity: Connect to data- kernels and spatial patterns Ref: Håkansson et al (2010). Advances in Complex Systems.

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

Preliminary results: range of network measures

Less data - • Need to generatenetworks with knowncharacteristics • Ifrelated to spatial patterns – measurepatterns of the nodes/holdings • Probablyneedlayers of spatial patterns – focal and regularnodes. Indicated by importance of productiontype. • alsorelates to slaughterhouses • Ifrelated to spatial kernels – measurekernelsbetweennodes/holdings • Probablyneed different kernels of and betweenlayers (productiontypes)

Less data – the route of a truck • Contact betweenholdingsdue to animal transport routes, for examplepicking up animals from different holdings on itsway to the slaugtherhouse. • We’vemade som algorthims to test different routeplanning. It turnsoutvery different depending on planningtools and aims. • Reduce transport distance by 30-40% • Another 30% ifreallocatebetweenslaughterhousesyet same capacity at eachslaughterhouse

Summing up • Lots of data- • Describetodayspattern • Predict today by yesterdays data • MCMC Bayesian sort out importance, distance production types etc • PPL – analyse and generate spatial pattern (pointpatterns) • 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

Contact patterns between herds: methods and visions (some results)