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Animal transport: spread of disease and …. Uno Wennergren Tom Lindström Annie Jonsson Nina Håkansson Jenny Lennartsson Spatio-Temporal Biology Division of Theoretical Biology Linköping University Sweden
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Animal transport 2006 - Aims of different projects The context – Research groups, their expertise – Data base on animal movements Specific research questions Estimating probability of animal movements – Tom Lindström
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Projects - aims - groups Spread of disease: Foot and mouth disease. – Prepare to optimize intervention Animal welfare – Reduce stress and distance transported
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Spread of disease: Foot and mouth disease. Funded by Swedish Civil Contingencies Agency (Swedish DHS): 2 grants, PI’s: UW and SSL at SVA – Prepare to optimize intervention Spatio-Temporal Biology (4 persons) – Biology/Ecology – Mathematics – Scientific Computing National Veterinary Institute (SVA) (3 persons) – Disease control and epidemiology – Veterinary medicine
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Animal welfare – Reduce stress and distance per animal Funded by Swedish Board of Agriculture (Swedish USDA) PI: UW Spatio-Temporal Biology (3 persons) – Biology/Ecology – Mathematics – Scientific Computing Dept. of Animal Environment and Health, Swedish University of Agricultural Sciences (2 persons) – Animal welfare – Veterinary medicine Skogforsk, LiU, NHH (3 persons) – Optimization –Logistics – route planning –
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Database All animal (cattle and pigs) movements between farms and farms to slaughterhouses. Not per vehicle – Cattle on individual level: birth, sale purchase, export, import, temporarily away (pasture), return from pasture, slaughter/house, death – Pig, on group level: as above Report within seven days Farms and slaughterhouses in Sweden. Dots: blue –farms, red – large slaughterhouses. Green - smaller slaughterhouses. From Håkansson et al 2007. Sweden
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Database -specifics 12 months - cattle approximately 1 000 000 reports of sales and purhase Important: errors in reports 10% – Possible to edit the database and reduce to 1% error by logical corrections (database cleaning) Spatial and temporal investigation of reported movements, births and deaths of cattle and pigs in Sweden. Submitted. Nöremark, Håkansson, Lindström, Wennergren, and Sternberg Lewerin.
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Specific research questions 1.Other contacts between farms - questionnaire to farmers (SVA) 2.From measured contacts to probability of contact 3.Spread: Modeling disease specifics 4.Route planning of animal transport – effect on contacts and movement distance. 5.Production units: composition and configuration 6.Networks 1.Analysing transport network 2.Testing efficiency of network measures as predictors 1.Generating netorks 2.Testing linkdensity on network formation 3.Testing measures as predictors
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1 2 ?
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Specific research questions From measured contacts to probability of contact Estimating probabilities Tom Lindström
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Animal movements between holdings Which farms are likely to have contacts through animal movements? – Mathematical description. – Estimation from data. Distance – Contacts between nearby farms are more common – Several different processes – Preventive Veterinary Medicine (any day now…)
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A word on the data Should be good… Pigs reported at transport level by the receiving farmer Cattle reported at individual level by farmers at both origin and end. – Cattle moved on the same day between same farms constitute one transport – Mismatch – “Cleaning” using the identity of cattle Locations of many cattle farms not in the database but areas of valid for subsidies Inactive farms in the data base
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Quantifying distance dependence Distance dependence needs two measurements. Probability of contacts has – Scale Measured as Variance (or Squared Displacement) – Shape Measured as Kurtosis
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Variance Distance P
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Kurtosis Distance P
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Why these measures? Important to have quantities for comparison – Between epidemics – Between types of contacts – Between years Theoretical connection to biological invasions – Squared displacement relates to diffusion constant. – Discrete representation of space (i.e. farms has X,Y coordinates) => Fat tails more important
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Kernel function A generalized normal distribution Variance and Kurtosis given by a and b. Extended to two dimensions (X,Y coordinates) – S normalizes the kernel, Volume=1.
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Kernel function normalization With discrete representation of farm distribution normalization over all possible destination farms d is distance, i is start farm, k is possible destination farms (k≠i) and N is number of farms.
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Kernel function normalization This separates spatial pattern of farms from distance dependence in contacts. Important if farm distribution is non random. Farm density in Sweden (farms/km 2 )
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And USA From Shields and Mathews, 2003
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Is the kernel function good enough? A single distribution may not be sufficient to fit data on multiple scales (both short and long distance contacts). An alternative model – A mixture model – Part distance dependent and part uniform (Mass Action Mixing) Models applied to pig and cattle transports (all transports during one year)..
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An alternative model f 1 is distance dependent part: f 2 is MAM part: w is proportion of distance dependence.
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Fitting to data Bayesian approach Increasingly common at least in ecological literature. Ellison 2008
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Markov Chain Monte Carlo Parameters obtained through Markov Chain Monte Carlo (MCMC). Well suitable for epidemiological problems. A simple model can be expanded to include complexity. Drawback is computation time, and effective parallelization is difficult.
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Markov Chain Monte Carlo Repeated (correlated) random draws from the posterior distribution of parameters. Gibbs Sampling – Direct draws from known distributions conditional on other parameter values Metropolis-Hastings – Values are proposed and subsequently accepted or rejected dependent on likelihood ratios
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Markov Chain Monte Carlo Also allows for model selection by comparing the full posterior distribution of model probabilities. In our study, the mixture model was a much better model. Pigs Cattle
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Comparing models and observed data Bars: observed transport distances. Dotted line: predictions by Model 1. Solid line: predictions by Model 2 CattlePigs
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Network measures Will differences have consequences for estimation of disease spread dynamics? Networks generated with the different models Network measures Nodes (farms) and links (transports) A B C D
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Network measures Density – proportion of farms connected Model 1 Model 2
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Network measures Clustering Coefficient – proportion of “triplets” – If A is connected to B and C, are B and C connected? A B C D Model 1 Model 2
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Network measures Fragmentation index – measures the amount of fragments not connected to the rest. A B C D E F D Model 1 Model 2
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Network measures Betweeness centralization index – Are some nodes more central than others? A B CD E F D A B CD E F D Model 1 Model 2
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Animal transports Higher Cluster Coefficient and lower Density for Model 2 – Depends on difference in short distance contacts – Depletion of susceptibles Group Betweeness higher for Model 1 in Cattle. – Due to long distance transport being more rare Conclusion: Model 2 is a better model (higher likelihood) and the difference may have impact on disease spread prediction.
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More than distance? Why not compare to observed networks? Is there something but distance that matter? Some work in progress…
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More than distance? Pig industry very structured, production types – Multiplying herd – Sow pool central unit – Sow pool satellite herd – Fattening herd – Farrow to finish herd – Piglet producing herd – Nucleus herd http://www.swedishmeats.com
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From To
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Production types in cattle? Dairy and beef producers Male calves on dairy farms are often sold to beef producers (at lest in Sweden) Other differences in production types? – Roping? – Organic farming? – Climate/geografic factors
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More than distance? Reality is messy… – Data base not perfect – Missing production types – Several production types per farms Weights in the model – A farm is a fraction of each possible type. One parameter estimation per combination (sender/receiver) of production types.
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More than distance? Size dependence – Size (Capacity) – Two different sizes Adult sows Piglets Different production types have different response – Different for sending or receiving – Total 64x4 parameters just for size… – Modeled as power function (Size θ )
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More than distance? Distance dependence – Different for different production types – Variance, Kurtosis and mixing parameter for each combination
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More than distance? Many parameters… 9*64=576 Some combinations of production types have few transports => uncertain estimations. Variance and kurtosis not clearly different from ∞. Using a prior may help – But it’s nicer to be objective…
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Hierarchical Bayesian We can let the data decide the prior – Hyper parameters Hierarchical Bayesian model “Borrowing strength”
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Animal transports – part 2 θ1θ1 θ2θ2 θ3θ3 θnθn Data P(θ )
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Hierarchical Bayesian When would this make sense? – If parameters values are expected to be different but not totally different – E.g. distance… Parameter estimations based on much data… – Little influence of hierarchical prior Parameter estimations with little data… – Highly influenced by the hierarchical prior. Increases the variance of the prior distribution.
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Thank you Questions?
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