SUPERBUGS:

1
SUPERBUGS

• The Mathematics of Epidemiology

2
Scope

• History and context
• School link
• Basic models
• Advances
• Questions

3
History

• 430BC Plague of Athens
• C14 Black Death
• 1854 London cholera epidemic halted
• 1867 Sir Joseph Lister introduces idea of
  antiseptic
• 1918-19 Influenza pandemic
• 1977 Last known case of smallpox
• 1978 UN Resolution Health for All 2000
• 1981 First recognition of HIV-1
• 2005 MRSA kills 3000 per year

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Figures
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Modelling (Kermack-McKendrick, 1927)

• S(t) No. of Susceptible individuals
• I(t) No. of Infective individuals
• R(t) No. of Removed individuals
• N Total population (assumed constant) S I
  R
• r gt 0 infection rate
• a gt 0 removal rate
• Assume negligible incubation period
• classes uniformly mixed

Susceptible
Infected
Removed
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Accuracy
Influenza epidemic, 1978
Bombay plague epidemic, 1905
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Issues to consider

• Predict disease spread and inform vaccination
  programmes
• Control drug dosage
• Statistical analysis of clinical tests
• Companies would be able to identify failing
  candidates and jettison them before they invest
  millions of dollars in costly clinical trials
• - Nature Medicine, 02/2006
• Simulation of chemical effects
• e-Therapeutics uses computers to
  mathematically analyse bacteria to find its
  weaknesses
• - The Journal, 16/1/2007

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Conclusions

• Relevant
• Accurate
• Non-trivial
• Necessary
• Interesting

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Questions?