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Mathematical modelling of epidemics among fish farms in the UK

Mathematical modelling of epidemics among fish farms in the UK. ISVEE 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 diseases

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Mathematical modelling of epidemics among fish farms in the UK

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  1. Mathematical modelling of epidemics among fish farms in the UK ISVEE X1 (2006) Cairns, Australia Kieran Sharkey The University of Liverpool

  2. 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 UniversityApplied Maths Dept Liverpool UniversityVeterinaryEpidemiology Group Lancaster UniversityStatistics Dept Stirling UniversityInstitute for Aquaculture CEFAS – Defra funded Laboratory

  3. Outline Pair-level equations and Foot&Mouth disease Application to fish farms Overview of modified model Results from new model applied to fish farm networks

  4. Remaining transmission is symmetric The Foot & Mouth Model Total animal movement ban

  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. Infection S I Removal R

  7. S

  8. I S SI Pair

  9. I S

  10. I S Insoluble

  11. I S Mean Field

  12. I S

  13. S S t I

  14. 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]

  15. B B B B A A A A C C C C + Triples Approximation

  16. Transmission routes between fish farms

  17. Nodes Fish farms

  18. Nodes Fish farms Fisheries

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

  20. Thames Test Avon Itchen Stour

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

  22. Route 2: Water flow (down stream)

  23. Route 2: Water flow (down stream)

  24. Transmission Mechanisms Foot&Mouth Fish disease Local Transportation Waterways Local Symmetric Non-symmetric Non-symmetric Symmetric Transmission Transmission Transmission Transmission Transmission routes fordisease

  25. General pair-wise model

  26. Asymmetric Contact Network A B C D 0 0 0 1 0 0 1 1 0 1 0 0 0 0 0 0 A B C D B C A D

  27. S I S←I S I S→I S I S↔I

  28. I S S -τ[I→S→S]

  29. S S I -τ[I→S→S] -τ[S→S←I]

  30. B B B A A A C C C +

  31. Some results from the model

  32. Nodes Fish farms Transport network (Live fish movement Database)

  33. 3576 0 65 65 1714 65 65 8 829 0 65 0 32 8 0 0 16 0 0 0 0 0 0 0

  34. Infectious Time Series

  35. Infectious Time Series

  36. Infectious Time Series

  37. Susceptible Time Series

  38. Summary Symmetric pair-wise equations generalise to include asymmetric transmission Asymmetric equations perform better on asymmetric networks.

  39. 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/s00285-006-0377-3

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