Mathematical modelling of epidemics among fish farms in the UK

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Mathematical modelling of epidemics among fish
farms in the UK

• ISVEE X1 (2006)
• Cairns, Australia
• Kieran Sharkey
• The University of Liverpool

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Funded by Defra (Department for Environment,
Food and Rural Affairs)
Investigate epidemiology of three fish
diseases IHN (Infectious Haematopoietic
Necrosis) VHS (Viral Haemorrhagic Septicaemia) GS
(Gyrodactylus Salaris)
Liverpool University Applied Maths Dept
Liverpool University Veterinary Epidemiology
Group Lancaster University Statistics
Dept Stirling University Institute for
Aquaculture CEFAS Defra funded Laboratory
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Outline
Pair-level equations and FootMouth disease
Application to fish farms
Overview of modified model
Results from new model applied to fish farm
networks
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The Foot Mouth Model
Total animal movement ban
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Contact Network
B
C
A
D
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Infection
S
I
Removal
R
7
S
8
I
S
SI Pair
9
I
S
10
I
S
Insoluble
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I
S
Mean Field
12
I
S
13
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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Transmission routes between fish farms
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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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Transmission routes fordisease
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General pair-wise model
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Asymmetric Contact Network
B
C
A
D
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S
I
S?I
S
I
S?I
S
I
S?I
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-tI?S?S
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-tS?S?I
-tI?S?S
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Some results from the model
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Nodes
Fish farms
Transport network (Live fish movement Database)
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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
Symmetric pair-wise equations generalise to
include asymmetric transmission
Asymmetric equations perform better on
asymmetric networks.
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Pair-level approximations to the
spatio-temporal dynamics of epidemics on
asymmetric contact networks Journal of
Mathematical Biology, Volume 53, Issue 1, Jul
2006, Pages 61 - 85, DOI 10.1007/s00285-006-0377-3
, URL http//dx.doi.org/10.1007/s00285-006-0377-
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