Infection Transmission Dynamics and Vaccination Program Effectiveness as a Function of Vaccine Effects in Individuals

  • Carl P. Simon
  • James S. Koopman
Conference paper
Part of the The IMA Volumes in Mathematics and its Applications book series (IMA, volume 126)


Ideal vaccine effect statistics should reflect biologically relevant parameters in an appropriate model of vaccine actions upon infection in the host. Ideal vaccine effectiveness statistics should reflect the effect of vaccination on the entire population or upon segments of that population such as vaccinated and unvaccinated individuals. The most commonly used vaccine effect statistic does not meet these ideals. It is one minus the risk in the vaccinated over the risk in the unvaccinated. These risks are sometimes calculated for disease and sometimes for infection. In this paper, we consider only infection. We label this statistic α and the risks in the vaccinated and unvaccinated populations on which it is based as R v and R u , respectively:
$$ \alpha = 1 - \frac{{{{R}_{v}}}}{{{{R}_{u}}}} = \frac{{{{R}_{{u - {{R}_{v}}}}}}}{{{{R}_{u}}}} = PAR\% $$


Reproduction Number Endemic Equilibrium Vaccine Trial Reproduction Dynamic Susceptibility Effect 
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Copyright information

© Springer Science+Business Media New York 2002

Authors and Affiliations

  • Carl P. Simon
    • 1
  • James S. Koopman
    • 2
  1. 1.Departments of Mathematics, Economics and Public Policy, Center for the Study of Complex SystemsUniversity of MichiganAnn ArborUSA
  2. 2.Department of Epidemiology, Center for the Study of Complex SystemsUniversity of MichiganAnn ArborUSA

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