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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. Animal transport 2006 - . Aims of different projects The context - PowerPoint PPT Presentation
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Animal transport: spread of disease and ….
Uno WennergrenTom Lindström
Annie JonssonNina Håkansson
Jenny Lennartsson
Spatio-Temporal BiologyDivision of Theoretical Biology
Linköping UniversitySweden
Animal transport2006 -
• 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
Projects - aims- groups
• Spread of disease: Foot and mouth disease. – Prepare to optimize intervention
• Animal welfare– Reduce stress and distance transported
• 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
• 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 –
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
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.
Specific research questions1. Other contacts between farms - questionnaire to
farmers (SVA)2. From measured contacts to probability of contact3. Spread: Modeling disease specifics4. Route planning of animal transport – effect on contacts and
movement distance.5. Production units: composition and configuration 6. Networks
1. Analysing transport network2. Testing efficiency of network measures as predictors
1. Generating netorks2. Testing linkdensity on network formation3. Testing measures as predictors
Gamma=0 Gamma=1 Gamma=2 Continuous landscapes
viewed from the
side
Continuous landscapes
viewed from above
Digitalized landscapes with 10% preferred habitat
Digitalized landscapes with 40% preferred habitat
1
2 ?
Specific research questionsFrom measured contacts to probability of contact
Estimating probabilities
Tom Lindström
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…)
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
Quantifying distance dependence
• Distance dependence needs two measurements. Probability of contacts has– Scale • Measured as Variance (or Squared Displacement)
– Shape• Measured as Kurtosis
Variance
Distance
P
Kurtosis
Distance
P
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
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.
Sebadg
b
ad
,
babS12
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.
1
1
N
k
ad b
ik
eS
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/km2)
And USA
From Shields and Mathews, 2003
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).
.
An alternative model
• f1 is distance dependent part:
• f2 is MAM part:
• w is proportion of distance dependence
tt dfwbadwf 21 1,
.
1
1
1 ,N
k
ad
ad
t bik
bt
e
ebadf
11
2 Ndf t
Fitting to data
• Bayesian approach• Increasingly common at least in ecological
literature.
Ellison 2008
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.
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
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
Comparing models and observed data
Bars: observed transport distances. Dotted line: predictions by Model 1. Solid line: predictions by Model 2
Cattle Pigs
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
Network measures
• Density – proportion of farms connected
Model 1 Model 2
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
Network measures
• Fragmentation index – measures the amount of fragments not connected to the rest.
A
B
C DE
FD
Model 1 Model 2
Network measures
• Betweeness centralization index – Are some nodes more central than others?
A
B
C D E
FD
A
B
C D E
FD
Model 1 Model 2
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.
More than distance?
• Why not compare to observed networks?• Is there something but distance that matter?• Some work in progress…
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
From
To
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
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.
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 (Sizeθ)
More than distance?
• Distance dependence– Different for different production types– Variance, Kurtosis and mixing parameter for each
combination
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…
Hierarchical Bayesian
• We can let the data decide the prior– Hyper parameters
• Hierarchical Bayesian model• “Borrowing strength”
Animal transports – part 2
θ1 θ2 θ3 θn
Data
P(θ )
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.
Thank you
• Questions?
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