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Mathematical modelling of epidemics among fish farms in
the UKISVEE X1 (2006)
Cairns, Australia
Kieran Sharkey
The University of Liverpool
Funded by Defra (Department for Environment, Food and Rural Affairs)
Investigate epidemiology of three fish diseasesIHN (Infectious Haematopoietic Necrosis)VHS (Viral Haemorrhagic Septicaemia)GS (Gyrodactylus Salaris)
Liverpool University Applied Maths Dept Liverpool University Veterinary Epidemiology GroupLancaster University Statistics DeptStirling University Institute for AquacultureCEFAS – Defra funded Laboratory
Pair-level equations and Foot&Mouth disease
Application to fish farms
Overview of modified model
Results from new model applied to fish farm networks
Outline
d[SS]/dt = -2[SSI]
d[SI]/dt = ([SSI]-[ISI]-[SI])-g[SI]
d[SR]/dt = -[RSI]+g[SI]
d[II]/dt = 2([ISI]+[SI])-2g[II]
d[IR]/dt = [RSI]+g([II]-[IR])
d[RR]/dt = 2g[IR]
Pair-wise Equations
Transmission routes fordisease
Transportation
Non-symmetric
Transmission
Waterways
Non-symmetric
Transmission
Fish disease
LocalSymmetricTransmission
Foot&Mouth
Transmission Mechanisms
LocalSymmetricTransmission
Summary
Symmetric pair-wise equations generalise to include asymmetric transmission
Asymmetric equations perform better on asymmetric networks.