1. Foot and Mouth Analysis Mike Delorme Rachelle Miron

2. Outline Foot and Mouth Information Discussion of Models analysis Summary Questions

3. Disease History Lots of information Disease that infects bovids (cows, pigs, goats, sheep...) Humans are very rarely affected It can be spread through the air or through contact There are vaccinations available Canada does not allow vaccination

4. http://www.csiro.au/images/mediaReleases/FMDtrottersmall.jpg http://www.mass.gov/agr/animalhealth/diseases/foot_mouth/pages/fmd_01.htm

5. 2001 UK Outbreak The 2001 Pre Budget Report estimated the direct economic impact of FMD at £2 billion - representing 0.2% of GDP. Tourism and related industries alone lost between £4.5 billion and £5.4 billion The 2001 outbreak took 221 days to eradicate, 1 day less than the outbreak of 1967-1968 By the end of the outbreak on September 30 2001, 6,094,139 animals had been killed - around two million for welfare reasons, and around four million for disease control purposes www.politics.co.uk Statistic 1: (Source: Treasury, Pre Budget Report 2001 (CM53182)); Statistics 2 and 3: (Source: DEFRA, 2004)

6. Spread Altered from http://news.bbc.co.uk/olmedia/1190000/images/_1193260_foot_mouth_25_03.gif http://news.bbc.co.uk/olmedia/1190000/images/_1193260_foot_mouth_25_03.gif

7. http://www.daffa.gov.au/animal-plant-health/animal/modelling/fmd

8. Building a Simple Model Worked with a SIR model Continuous time

9. Susceptible Born susceptible Can become infected Can die naturally

10. Infected Enter from S Can die naturally Can die from disease Can recover

11. Recovered Can die naturally Can lose their immunity Become susceptible again

12. Model 1 – The Basics

13. Model 1 - Analysis Set Infected=0 to get disease free equilibrium DFE Set up Jacobian and evaluate at DFE Arino Method Examines infected cows in the system Gives R 0 value for model Find I* Plot S,I,R vs. time

14. Model 1 - Equations

15. Model 1

16. Model 1 - Analysis Values for parameters

17. Model 1 – R 0 >1

19. Model 1 - R 0 <1

20. Model 1 – R 0 <1

21. Model 2 – More Infections

23. Model 2 - Equations

24. Model 2 - Analysis

25. Model 2 – Parameter Values

26. Model 2 – R 0 >1

27. Model 2 – R 0 <1

28. Model 3 - Vaccine Can vaccinate cows so they never get the disease Low numbers of susceptible cows at equilibrium can represent cows leaving the system due to vaccination

29. Model 3

30. Model 3 - Analysis What will happen when different proportions of cattle are vaccinated?

31. Model 3 - Equations

33. Model 3 – Parameter values

34. Model 3 – R 0 >1

35. Model 3 – R 0 >1 - Zoomed

36. Model 3 – R 0 < 1

37. Model 3 - Analysis Very few Susceptible cows left Where have they gone?

38. Model 4 – Vaccine++ How many cows are vaccinated? Set up a “Perfect” class that keeps track of immunized cows How many cows need to be vaccinated to have no infected cows at equilibrium? Herd Immunity

39. Perfect Cows (P) Created by vaccinating newborn cows vaccinating cows after they recover from the disease Leave due to natural death www.uoguelph.ca

40. Model 4

41. Model 4 - Equations

42. Note: Same R 0 as in Model 3 Same parameter values as in Model 3

43. Model 4 – R 0 >1

44. Model 4 – R 0 >1 Zoomed

45. Model 4 – R 0 < 1

46. Model 5 – Keep track of dead Improvement on Model 4 Now cows that die as a result of the disease are tracked Z for Zombie

47. Model 5

48. Model 5 - Equations

49. Note: Same DFE and R 0 as in Model 4 Same parameter values as in Model 3

50. Model 5 – R 0 >1

51. Model 5 – R 0 <1

52. Herd Immunity What % of the population do you need to vaccinate in order to effectively stop the disease? Depends on vaccine and disease Polio, small pox... Assume there is 1 type of virus Assume the vaccine works 100% of the time and as soon as administered

53. Herd Immunity We found this when going from Model 2 to Model 3 When we introduced vaccination

54. Herd Immunity Plot I* vs. p see where the line crosses I*=0 For disease to die out

55. I* vs. p

56. What next? Different ages Different virus strains Different vaccination strategies Ring vaccination Economic strategy Cost of killing a cow vs. Cost of vaccination

57. Does it make cents to vaccinate? Cow costs ~$2190.90 Profit per cow ~$549.99 Vaccinate ~$47.74 Bates et al. Benefit:Cost ~10:1 Mike & Rachelle Benefit:Cost~11.5:1

58. Summary The spread of Foot and Mouth can be modelled with a SIR type model Analysis can determine the level of vaccination required to keep a cow immune Equations can get complicated

59. Sources Pech, R. & Hone, J. (1988) A model of the dynamics and control of an outbreak of foot and mouth disease in feral pigs in Australia. Journal of Applied Ecology, 25, 63-77. http://www.jstor.org/view/00218901/di996048/99p02395/0 http://www.jstor.org/view/00218901/di996048/99p02395/0 Bates, T. & Carpenter, T. & Thurmond, M. (2003) Benefit-cost analysis of vaccination and preemptive slaughter as a means of eradicating foot- and-mouth disease. Vol. 64, No. 7, Pg 805-812. http://avmajournals.avma.org/doi/abs/10.2460/ajvr.2003.64.805?cookie Set=1&journalCode=ajvr http://avmajournals.avma.org/doi/abs/10.2460/ajvr.2003.64.805?cookie Set=1&journalCode=ajvr Kaneene, J. & Miller,R. (1995) Risk factors for metritis in Michigan dairy cattle using herd- and cow-based modelling approaches. Preventive Veterinary Medicine, Volume 23, Number 3, pp. 183-200. http://www.ingentaconnect.com/content/els/01675877/1995/00000023/0 0000003/art00438 http://www.ingentaconnect.com/content/els/01675877/1995/00000023/0 0000003/art00438 How Much for that Cow? BBC News. David Brown, secretary of the Livestock Auctioneers Association. http://news.bbc.co.uk/1/hi/uk/1476141.stm http://news.bbc.co.uk/1/hi/uk/1476141.stm