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
http://www.csiro.au/images/mediaReleases/FMDtrottersmall.jpg
http://www.mass.gov/agr/animalhealth/diseases/foot_mouth/pages/fmd_01.htm
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
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Statistic 1: (Source: Treasury, Pre Budget Report 2001 (CM53182)); Statistics 2 and 3: (Source: DEFRA, 2004)
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
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
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
Perfect Cows (P)
Created by vaccinating newborn cows vaccinating cows after
they recover from the disease Leave due to natural death
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Model 4 - Equations
),0,0,0,)1(
(),,,,(
pp
PRIDS
m
rmrpR i
)(
)()1(0
Note: Same R0 as in Model 3
Same parameter values as in Model 3
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
Model 5 - Equations
)0,,0,0,0,)1(
(),,,,,(
pp
ZPRIDS
m
rmrpR i
)(
)()1(0
Note: Same DFE and R0 as in Model 4
Same parameter values as in Model 3
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
20
30 )1( ModelModel RpR
130 ModelR
Herd Immunity
We found this when going from Model 2 to Model 3 When we introduced vaccination
What next?
Different ages Different virus strains Different vaccination strategies
Ring vaccination Economic strategy
Cost of killing a cow vs. Cost of vaccination
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
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
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
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?cookieSet=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/01675877/1995/00000023/00000003/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