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Modelling the effect of a booster vaccination on disease epidemiology

Journal of Mathematical Biology volume 52, pages 290–306 (2006)Cite this article

Abstract

Despite the effectiveness of vaccines in dramatically decreasing the number of new infectious cases and severity of illnesses, imperfect vaccines may not completely prevent infection. This is because the immunity afforded by these vaccines is not complete and may wane with time, leading to resurgence and epidemic outbreaks notwithstanding high levels of primary vaccination. To prevent an endemic spread of disease, and achieve eradication, several countries have introduced booster vaccination programs. The question of whether this strategy could eventually provide the conditions for global eradication is addressed here by developing a seasonally-forced mathematical model. The analysis of the model provides the threshold condition for disease control in terms of four major parameters: coverage of the primary vaccine; efficacy of the vaccine; waning rate; and the rate of booster administration. The results show that if the vaccine provides only temporary immunity, then the infection typically cannot be eradicated by a single vaccination episode. Furthermore, having a booster program does not necessarily guarantee the control of a disease, though the level of epidemicity may be reduced. In addition, these findings strongly suggest that the high coverage of primary vaccination remains crucial to the success of a booster strategy. Simulations using estimated parameters for measles illustrate model predictions.

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Author information

Affiliations

  1. Institute for Biodiagnostics, National Research Council Canada, R3B 1Y6, Winnipeg, Manitoba, Canada

    M.E. Alexander, S.M. Moghadas & A.R. Summers

  2. Institute of Ecology, University of Georgia, Athens, GA, 30602-2202, USA

    P. Rohani

Authors
  1. M.E. Alexander
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  2. S.M. Moghadas
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  3. P. Rohani
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  4. A.R. Summers
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Corresponding author

Correspondence to M.E. Alexander.

Additional information

This work was supported in part by the Natural Sciences and Engineering Research Council of Canada (NSERC). One of the authors (P.R.) acknowledges the support of the Ellison Medical Foundation.

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Alexander, M., Moghadas, S., Rohani, P. et al. Modelling the effect of a booster vaccination on disease epidemiology. J. Math. Biol. 52, 290–306 (2006). https://doi.org/10.1007/s00285-005-0356-0

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  • DOI: https://doi.org/10.1007/s00285-005-0356-0

Key words or phrases

  • Basic reproductive number
  • Epidemic models
  • Floquet theory
  • Equilibria
  • Stability
  • Vaccination