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

Contact patterns between herds: methods and visions

(some results)

Uno Wennergren(Tom Lindström)

Linköping UniversitySweden

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

• Spatial distribution of premises

• Contact between premises

AB

C D E

FG

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 BayesianCutting edge statistics

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’

T

tt badfbadP

11 ,,

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 !

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

Sow Pool Center

SatellitesBreeding pyramid Sow pool

Farrow-to-finish

Farrow-to-finish

Production typeTO

FROM

Sow pool center

Sow pool satellite Farrow-to-finish

Nucleusherd

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

Distance

Bars: Observed movement distances; Dotted line: Spatial kernel (Simpler model); Solid line: Spatial kernel + uniform part (Mixture model)

Cattle Pigs


Distance

• Known as– Generalized normal distribution– Power exponential distribution

SeP

b

ad

P: contact probabilityd: distancea,b: regulates shape and scaleS: 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

P UwwP 1

SeP

b

ad

Agenda


Production type

• More than one type per holding

Estimates of v0.04=

0.0023)+(0.0520.0023

0.96=0.0023)+(0.052

0.052


Production type

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

• Simulation

Sow Pool Center

Satellites

Farrow-to-finish


Production type

Agenda


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


Lindström et al. Prev. Vet. Med. In press


• Hierarchical priors for distance parameters

D1 D2 D3 Dn

θ1 θ2 θ3 θn

ξ


• 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…Sow pool

center

Sow pool

satellite

Farrow-

to-finish

Nucleus

herd

Piglet

producer

Multiplying

herd

Fattening

herd

Missing

information

Outgoing

Fattening pigs0.043 -0.035 -0.033 0.18 -0.0049 0.021 0.36 -0.44

Outgoing

Sows0.31 0.24 0.67 0.69 0.47 0.44 0.68 -0.29

Incoming

Fattening pigs0.029 0.091 -0.034 1 0.045 -0.013 0.51 -1.2

Incoming

Sows0.37 0.15 0.52 -0.86 0.66 0.26 0.12 0.15

Lindström et al. Prev. Vet. Med. In press


• Distance dependence differs between production types

Green: Sow pool centersto satellites

Blue: Nucleus toMultiplying herds

Red: Farrow-to-finishto Fattening herds


• Good fit with observed distances

Distance

Prop

ortio

n of

mov

emen

ts

Agenda


Influence on disease spread dynamics

• Effect of production type, herd size and between herd distance.

• Simulate disease spread with reduced models1. Mass action mixing2. Full model3. No production type structure4. No herd size effect5. No distance dependence6. No production type difference in distance dependence


• Mean nr of infected vs. time

Lindström et al. Forthcoming


• 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 shape

depend on the spatial arrangement of farms?

• Description of the point pattern distribution– Spectral representation

Spectral representation

Contrast: 4.9Continuity: 2.0




– Continuity • Spatial autocorrelation

– Contrast• Difference in density


• Simulation with different scale and shape– Distance– Nr infected

Lindström et al, Proc. Roy. Soc. Lond. B. In press.


• How to implement distance dependence of infection probability?– Absolute or Relative

Contrast

Conti

nuity

Conti

nuity

Piglet producers to Fattening herds

Agenda


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)?

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)?

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?

• 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?

• 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

• 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

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

asso

rtati

vity

Clus

terin

g co

effici

ent

Lennartsson et al. manuscript

Link density

Link densityNot the best set of links?Other conditions?Adding links – more data?

Other conditionsspatial patterns - kernels

• Not studied yet-

need methods to generate the conditionsthe spatial patterns (patially solved)the spatial kernels (solved)

networks metrics that spans the empirically found intervals

Network algorithmSpec 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

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

Spec Net1

Spec Net2

CM 1

CM 2

Clustering coefficient

0.01 -0.80 0.01 – 0.81 0.01 – 0.25 0.01 – 0.25

Fragmentation index

0.00 – 0.97 0 – 0.96 0 – 0.20 0 – 0.19

Assortativity -0.10 – 0.85 -0.69 – 0.88 -0.25 – 0.08 -0.64 – 0.04

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)

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

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

Documents

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