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Smallpox

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Royal family tested variolation on condemned prisoners and when found successful ... present then it would produce 8000 20 year olds under an inoculation system ... – PowerPoint PPT presentation

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Title: Smallpox


1
Smallpox
  • circa 1718 method of variolation brought to
    England by Lady Mary Wortley Montagu, wife of the
    Turkish ambassador, Edward Wortley Montagu
  • 1721 epidemic in London
  • Royal family tested variolation on condemned
    prisoners and when found successful they
    inoculated themselves
  • variolation slow to be accepted
  • 1796 Edward Jenner introduced a smallpox vaccine
    using cowpox fluid

2
Daniel Bernoullis Smallpox Analysis
  • Assumptions
  • p, the risk of contracting smallpox is the same
    at every age (p 1/8)
  • p, the risk of dying from smallpox is the same at
    every age (p 1/8)

3
Notation
4
Bernoullis Differential Equation
5
The Competing Risk Model
Assuming a 1/8 probability of contracting
smallpox among those at risk and a 1/8
probability of death among those contracting
smallpox Bernoulli obtained
The solution to the differential equation yields
6
Halleys Life Table, 1693
Bernoullis Life Table Analysis with Smallpox
7
Gain Due to Inoculation
  • Bernoulli noted that the asymptotic gain was
    approximately 7 to 8
  • argued that if Paris produced 7000 20 year olds
    per yield with smallpox present then it would
    produce 8000 20 year olds under an inoculation
    system
  • likewise if the civil births for the whole of
    France was 175000 then it would be 200000 without
    smallpox so that France would gain 25000 persons
    every year, all useful to the State and to
    society

8
Laplaces Summary of DAlemberts Objections to
Bernoulli
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