Bayesian spatial modelling of disease vector data on Danish farmland Carsten Kirkeby Gerard Heuvelink Anders Stockmarr René Bødker.

Bayesian spatial modelling of disease vector data on Danish farmland

Carsten KirkebyGerard HeuvelinkAnders StockmarrRené Bødker

Biting midges

• Culicoides obsoletus group

• Bloodsucking females

• 1400 species ~ 40 in Denmark

• 1-2mm

• Parasites: protozoans, nematodes

• Virus: African Horse Sickness,

Akabane Virus etc.

Institute of Animal Health UK

Bluetongue virus

• Midge-borne

• Infects ruminants

• Northern Europe: 2006-2010

• Symptoms: Fever, diarrhoea, reduced milk production

Institute of Animal Health UK

Schmallenberg virus

• Midge-borne

• Infects ruminants

• Northern Europe: 2011 - ?

• Symptoms: Fever, stillbirths, malformations, reduced milk production

Institute of Animal Health UK

Aim

How are vectors distributed in farmland?

• Host animals• Tree cover• Temporal covariates

• High/low risk areas• Optimization of vector surveillance• Input for simulation models

Field study

x

Field study

823000 824000 825000

61

38

50

06

13

90

00

61

39

50

06

14

00

00

61

40

50

0

ny.x

ny.

y x

x

x

x

xx

x

x

xx

x

x

x

x x

x

x

x

xx

x

x

x

x

x

x

823000 824000 825000

61

38

50

06

13

90

00

61

39

50

06

14

00

00

61

40

50

0

ny.x

ny.

y 2

0

12

241

100

198

0

610

1

1

162

0 0

14

0

68

240247

26

0

0

45

0

0

Field study

Data

Analysis

Count data

Analysis

Spatial component

“Your neighbours influence you, but you also influence your neighbours.”

Charles Manski 

Analysis

Temporal component

t

t-1

Analysis

R: geoRglm package – GLGM krigingpois.krige.bayes()

Bayesian kriging for the poisson spatial model

Y ~ β + S(ρ) + ε

β = + + + + dayeffect + lag1

Analysis

Spatial correlation: Matérn covariance function

Φ

Analysis - separate

Analysis - simultaneous

Distance to cattle farm

Den

sity

-1.6 -1.4 -1.2 -1.0 -0.8 -0.6

0.0

0.5

1.0

1.5

2.0

Distance to pig farm

Den

sity

-1.2 -1.0 -0.8 -0.6 -0.4 -0.2

0.0

0.5

1.0

1.5

2.0

2.5

Distance to angus farm

Den

sity

-1.2 -1.0 -0.8 -0.6 -0.4 -0.2

0.0

0.5

1.0

1.5

2.0

Distance to forest

Den

sity

-0.002 0.000 0.002 0.004

010

020

030

040

0

Analysis - simultaneous

Distance to cattle farm

Den

sity

-1.4 -1.2 -1.0 -0.8 -0.6

0.0

1.0

2.0

3.0

Distance to pig farm

Den

sity

-1.0 -0.8 -0.6 -0.4 -0.2 0.0

0.0

0.5

1.0

1.5

2.0

2.5

Distance to angus farm

Den

sity

-1.4 -1.0 -0.6 -0.2 0.0

0.0

0.5

1.0

1.5

2.0

Correlation with previous catch

Den

sity

0.020 0.025 0.030 0.035

050

100

150

Analysis - comparison

Distance to cattle farm

Den

sity

-1.4 -1.2 -1.0 -0.8 -0.6

0.0

1.0

2.0

3.0

Distance to pig farm

Den

sity

-1.0 -0.8 -0.6 -0.4 -0.2 0.0

0.0

0.5

1.0

1.5

2.0

2.5

Distance to angus farm

Den

sity

-1.4 -1.0 -0.6 -0.2 0.0

0.0

0.5

1.0

1.5

2.0

Correlation with previous catch

Den

sity

0.020 0.025 0.030 0.035

050

100

150

-0.12 -0.33

0.07 0.008

Non-spatialPoissonregression

Analysis - prediction

0.5

1.0

1.5

2.0

2.5

C

P

A

Predicted average vector density

1 km

Analysis – temporal covariatesDistance to cattle farm

Den

sity

-1.8 -1.4 -1.0 -0.6

0.0

0.5

1.0

1.5

Distance to pig farm

Den

sity

-1.4 -1.0 -0.6 -0.2

0.0

0.5

1.0

1.5

Distance to angus farm

Den

sity

-1.5 -1.0 -0.5 0.0

0.00.20.40.60.81.01.2

Distance to forest

Den

sity

-0.003 -0.001 0.001 0.003

0

100

200

300

400

Lag1

Den

sity

0.010 0.020 0.030

0

50

100

150

Temperature (C)

Den

sity

0.2 0.4 0.6 0.8 1.0 1.2 1.4

0.0

0.5

1.0

1.5

2.0

Humidity

Den

sity

-0.2 -0.1 0.0 0.1

0123456

Wind speed (m/s)

Den

sity

-3.0 -2.5 -2.0 -1.5 -1.0

0.00.20.4

0.60.81.0

Rain (mm)

Den

sity

-0.3 -0.2 -0.1 0.0 0.1 0.2

012345

Turbulence

Den

sity

-0.2 -0.1 0.0 0.1

0

2

4

6

8

Phi

Den

sity

20 40 60 80 100

0.000

0.005

0.010

0.015

0.020

Findings

• Quantify effects of cattle and pigs

• No effect of forests

• Quantify temporal covariates

• Weak positive correlation with previous catch

• More vectors at the pig farm than the cattle farm

Future

•Jackknife

•Validation on other dataset

Acknowledgements

Thanks:

• Ole Fredslund Christensen

• Astrid Blok van Witteloostuijn

Thank you for your attention

Carsten [email protected]