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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
