Foot and Mouth Analysis

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

7. http://www.daffa.gov.au/animal-plant-health/animal/modelling/fmdhttp://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 R0 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 – R0>1

18. Model 1 – R0>1

19. Model 1 - R0<1

20. Model 1 – R0 <1

21. Model 2 – More Infections

22. Model 2 – More Infections

23. Model 2 - Equations

24. Model 2 - Analysis

25. Model 2 – Parameter Values

26. Model 2 – R0 >1

27. Model 2 – R0 <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

32. Model 3 - Equations

33. Model 3 – Parameter values

34. Model 3 – R0 >1

35. Model 3 – R0 >1 - Zoomed

36. Model 3 – R0 <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. Model 4 - Equations Note: Same R0 as in Model 3 Same parameter values as in Model 3

43. Model 4 – R0 >1

44. Model 4 – R0 >1 Zoomed

45. Model 4 – R0 <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. Model 5 - Equations Note: Same DFE and R0 as in Model 4 Same parameter values as in Model 3

50. Model 5 – R0 >1