Spatio-temporal dynamics, fish farms and pair-approximations

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Spatio-temporal dynamics, fish farms and
pair-approximations

• Maths2005
• The University of Liverpool
• Kieran Sharkey, Roger Bowers, Kenton Morgan

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Collaboration between Liverpool University
Veterinary Epidemiology Group Liverpool
University Applied Maths Dept Lancaster
University Statistics Dept Stirling University
Institute for Aquaculture CEFAS Defra funded
Laboratory
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Outline
The symmetric pair-wise model and FootMouth
disease
Application to fish farms
Overview of non-symmetric model
Results from non-symmetric model applied to fish
farm data
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The Symmetric Pair-wise model
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Contact Network
B
C
A
D
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2001 FootMouth Outbreak
Total ban on livestock movement
Route of transmission assumes to be local
symmetric
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S
8
S
S
t
I
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Pair-wise Equations
dSS/dt -2?SSI dSI/dt
?(SSI-ISI-SI)-gSI dSR/dt
-?RSIgSI dII/dt 2?(ISISI)-2gII
dIR/dt ?RSIg(II-IR) dRR/dt
2gIR
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Triples Approximation
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Disease transmission between fish farms
Slides in this section provided by Mark Thrush at
CEFAS
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Disease transmission matrix

• Nodes
• Fish Farms
• Fisheries
• Wild populations

• Routes of transmission
• Live fish movement
• Water flow
• Wild fish migration
• Fish farm personnel equipment

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?
?
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Nodes
Fish farms
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Nodes
Fish farms
Fisheries
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Nodes
Fish farms
Fisheries
Wild fish (EA sampling sites)
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Thames
Test
Avon
Itchen
Stour
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Route 1 Live Fish Movement
Thames
Test
Avon
Itchen
Stour
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Route 2 Water flow (down stream)
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Route 2 Water flow (down stream)
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General pair-wise model
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Contact network eg
0 1 1 1 0 0 0 1 0
G

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S
I
S?I
S
I
S?I
S
I
S?I
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Some results from the model
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Nodes
Fish farms
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3576
0
65
65
1714
65
65
8
829
0
65
0
32
8
0
0
16
0
0
0
0
0
0
0
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Infectious Time Series
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Infectious Time Series
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Infectious Time Series
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Susceptible Time Series
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Summary
The symmetric pair-wise equations can be
generalised to include asymmetric transmission.

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Summary
The non-symmetric model can give significantly
different predictions to the symmetric model.
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Summary
The non-symmetric model is closer to stochastic
simulation than the symmetric model on one
non-symmetric network.