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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)

Abstract

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:
$$ \alpha = 1 - \frac{{{{R}_{v}}}}{{{{R}_{u}}}} = \frac{{{{R}_{{u - {{R}_{v}}}}}}}{{{{R}_{u}}}} = PAR\% $$
(1)

Keywords

Reproduction Number Endemic Equilibrium Vaccine Trial Reproduction Dynamic Susceptibility Effect 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    Eichner M. and K.P. Hadeler, “Deterministic Models for the Eradication of Poliomyelitis: Vaccination with the Inactivated (IPV) and Attenuated (OPV) Polio Virus Vaccine.” Mathematical Biosciences (1995), 127: 149–166.zbMATHCrossRefGoogle Scholar
  2. [2]
    Haber M., “Estimation of the direct and indirect effects of vaccination.” Statistics in Medicine (1999), 18: 2101–2109.CrossRefGoogle Scholar
  3. [3]
    Koopman J.S., J.A. Jacquez, C.P. Simon, et al., “The Role of Primary HIV Infection in the Spread of HIV Through Populations,” Journal of A.I.D.S. (1997), 14: 249–258.Google Scholar
  4. [4]
    Koopman J.S. and R.J. Little, “Assessing HIV Vaccines Effects,” Amer. J. Epid. (1995), 142: 1113–1120.Google Scholar
  5. [5]
    Longini I.M. and M.E. Halloran, “A Frailty Mixture Model for Estimating Vaccine Efficacy.” Appl Statist (1996), 45: 165–73.zbMATHCrossRefGoogle Scholar
  6. [6]
    Metz J.A.J. and O. Diekmann (eds.), The Dynamics of Physiologically Structured Populations. Springer Verlag Lecture Notes in Biomathematics (1986), 68.zbMATHGoogle Scholar
  7. [7]
    Rothman K. and S. Greenland, Modern Epidemiology, Second Edition. Lippincott, Williams and Wilkins (1998).Google Scholar
  8. [8]
    Simon C.P. and J.A. Jacquez, “Reproduction Numbers and the Stability of Equilibria of SI Models for Heterogeneous Populations.” S.I.A.M. Journal of Applied Mathematics (1992), 52(2): 541–576.MathSciNetzbMATHCrossRefGoogle Scholar
  9. [9]
    Simon C.P., J.A. Jacquez, and J.S. Koopman, “A Liapunov Function Approach to Computing R 0.” Models for Infectious Diseases (V. Isham & G. Medley, eds.) Cambridge University Press (1995).Google Scholar
  10. [10]
    Smith P.G., Rodriguez L.C., and Fine P.E., “Assessment of the Protective Efficacy of Vaccines Against Common Diseases Using Case-Control and Cohort Studies.” International Journal of Epidemiology (1984), 13(1): 87–93.CrossRefGoogle Scholar

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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