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Spatio-temporal dynamics, fish farms and pair-approximations

Spatio-temporal dynamics, fish farms and pair-approximations. Maths2005 The University of Liverpool Kieran Sharkey, Roger Bowers, Kenton Morgan. DEFRA funded. Investigate epidemiology of three fish diseases IHN (Infectious Haematopoietic Necrosis) VHS (Viral Haemorrhagic Septicaemia)

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Spatio-temporal dynamics, fish farms and pair-approximations

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  1. Spatio-temporal dynamics, fish farms and pair-approximations Maths2005 The University of Liverpool Kieran Sharkey, Roger Bowers, Kenton Morgan

  2. DEFRA funded Investigate epidemiology of three fish diseases IHN (Infectious Haematopoietic Necrosis) VHS (Viral Haemorrhagic Septicaemia) GS (Gyrodactylus Salaris) Collaboration between: Liverpool UniversityVeterinaryEpidemiology Group Liverpool UniversityApplied Maths Dept Lancaster UniversityStatistics Dept Stirling UniversityInstitute for Aquaculture CEFAS – Defra funded Laboratory

  3. Outline The symmetric pair-wise model and Foot&Mouth disease Application to fish farms Overview of non-symmetric model Results from non-symmetric model applied to fish farm data

  4. The Symmetric Pair-wise model

  5. A B C D 0 0 0 1 0 0 1 1 0 1 0 0 1 1 0 0 A B C D Contact Network B C A D

  6. 2001 Foot&Mouth Outbreak Total ban on livestock movement Route of transmission assumes to be local & symmetric

  7. I S

  8. S S t I

  9. Pair-wise Equations 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]

  10. B B B B A A A A C C C C + Triples Approximation

  11. Disease transmission between fish farms Slides in this section provided by Mark Thrush at CEFAS

  12. Nodes Fish Farms Fisheries Wild populations Routes of transmission Live fish movement Water flow Wild fish migration Fish farm personnel & equipment Disease transmission matrix   ?

  13. Nodes Fish farms

  14. Nodes Fish farms Fisheries

  15. Nodes Fish farms Fisheries Wild fish (EA sampling sites)

  16. Thames Test Avon Itchen Stour

  17. Route 1: Live Fish Movement Thames Test Avon Itchen Stour

  18. Route 2: Water flow (down stream)

  19. Route 2: Water flow (down stream)

  20. General pair-wise model

  21. 0 1 0 1 0 0 0 0 0 0 0 1 0 0 0 0 1 0 Gs = Ga = Contact network: eg 0 1 1 1 0 0 0 1 0 G =

  22. S I S←I S I S→I S I S↔I

  23. B B B A A A C C C +

  24. Some results from the model

  25. Nodes Fish farms

  26. 3576 0 65 65 1714 65 65 8 829 0 65 0 32 8 0 0 16 0 0 0 0 0 0 0

  27. Infectious Time Series

  28. Infectious Time Series

  29. Infectious Time Series

  30. Susceptible Time Series

  31. Summary The symmetric pair-wise equations can be generalised to include asymmetric transmission.

  32. Summary The non-symmetric model can give significantly different predictions to the symmetric model.

  33. Summary The non-symmetric model is closer to stochastic simulation than the symmetric model on one non-symmetric network.

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