To Vaccinate or Not to Vaccinate

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To Vaccinate or Not to Vaccinate?

• That is the question

Joanne Mann J.L.Mann_at_Massey.ac.nz
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Vaccine-Preventable Diseases

• Cholera
• Dengue
• Diphtheria
• E coli
• Influenza
• Haemophillus influenzae B
• Hepatitis A
• Hepatitis B
• Human Papillomavirus
• Japanese encephalitis
• Measles
• Meningococcus
• Mumps
• Tetanus/Neonatal tetanus

• Pertussis (whooping cough)
• Pneumococcus
• Poliomyelitis
• Rabies
• Rotavirus
• Rubella
• Shigella
• Smallpox
• Tuberculosis
• Typhoid
• Yellow fever
• Varicella (chickenpox)
• Vitamin A
• Other diseases

Source http//www.who.int/vaccines/en/vaccprevdi
s.shtml
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Why Be Vaccinated?

• So that you dont get infected.
• So that you dont pass the infection on.
• But
• What about the negative side effects from a
  vaccination?

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Should I be Vaccinated?

• It depends on the relative costs of remaining
  susceptible and of being vaccinated.
• But, if everyone around you is vaccinated

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On To the Maths

• Let p be the proportion of the population that
  are vaccinated (then 1-p arent vaccinated).
• Let Cv be the cost of being vaccinated, and Cs be
  the cost of remaining susceptible.
• Let S8 be the proportion of the population that
  are still susceptible after an epidemic.

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On To the Maths

• S8 is calculated from
• R0 is the basic reproduction ratio the number of
  secondary cases that would occur from a primary
  case in a fully susceptible population.

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Two Choices

• Be vaccinated, then your expected individual cost
  is Cv.
• Remain susceptible, then your expected individual
  cost is
• 1-p-S8 is the proportion of the population who
  were infected during the epidemic.

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The Community

• The cost to the community will be a combination
  of the two individual strategies
• What is the best option?

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The Best Individual Strategy

• The best strategy for the individual varies
  depending on Cv and Cs.
• If Cv lt Cs then the expected cost of vaccination
  is lower than the cost of remaining susceptible,
  unless a significant proportion of the population
  is vaccinated.
• Best Strategy

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Best for the Community

• The lowest expected cost, for the community, is
  to always vaccinate the proportion of the
  population equal to
• So, convince every one you come in contact with
  to be vaccinated then you dont have to be!

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References

• Bauch, C. T., Galvani, A. P. and Earn, D. J.
  Group Interest Versus Self-Interest in Smallpox
  Vaccination Policy. Proc Natl Acad Sci U S A.
  2003 Sep 2100(18)10564-7 (available online
  http//www.pubmedcentral.nih.gov/articlerender.fcg
  i?toolpubmedpubmedid12920181)
• Mann, J. Modelling repeated epidemics with
  general infection kernels.