Foot and Mouth Analysis Mike Delorme Rachelle Miron

Outline Foot and Mouth Information Discussion of Models analysis Summary Questions

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

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 By the end of the outbreak on September , 6,094,139 animals had been killed - around two million for welfare reasons, and around four million for disease control purposes Statistic 1: (Source: Treasury, Pre Budget Report 2001 (CM53182)); Statistics 2 and 3: (Source: DEFRA, 2004)

Spread Altered from

Building a Simple Model Worked with a SIR model Continuous time

Susceptible Born susceptible Can become infected Can die naturally

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

Recovered Can die naturally Can lose their immunity Become susceptible again

Model 1 – The Basics

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

Model 1 - Equations

Model 1

Model 1 - Analysis Values for parameters

Model 1 – R 0 >1

Model 1 - R 0 <1

Model 1 – R 0 <1

Model 2 – More Infections

Model 2 - Equations

Model 2 - Analysis

Model 2 – Parameter Values

Model 2 – R 0 >1

Model 2 – R 0 <1

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 3

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

Model 3 - Equations

Model 3 – Parameter values

Model 3 – R 0 >1

Model 3 – R 0 >1 - Zoomed

Model 3 – R 0 < 1

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

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

Model 4

Model 4 - Equations

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

Model 4 – R 0 >1

Model 4 – R 0 >1 Zoomed

Model 4 – R 0 < 1

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

Model 5 - Equations

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

Model 5 – R 0 >1

Model 5 – R 0 <1

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

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

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

I* vs. p

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 ~$ Profit per cow ~$ 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, 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 Set=1&journalCode=ajvr 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 /art /art00438 How Much for that Cow? BBC News. David Brown, secretary of the Livestock Auctioneers Association.