Journal of Mathematical Biology

, Volume 68, Issue 4, pp 969–987

The evolutionary consequences of alternative types of imperfect vaccines


DOI: 10.1007/s00285-013-0654-x

Cite this article as:
Magori, K. & Park, A.W. J. Math. Biol. (2014) 68: 969. doi:10.1007/s00285-013-0654-x


The emergence and spread of mutant pathogens that evade the effects of prophylactic interventions, including vaccines, threatens our ability to control infectious diseases globally. Imperfect vaccines (e.g. those used against influenza), while not providing life-long immunity, confer protection by reducing a range of pathogen life-history characteristics; conversely, mutant pathogens can gain an advantage by restoring the same range of traits in vaccinated hosts. Using an SEIR model motivated by equine influenza, we investigate the evolutionary consequences of alternative types of imperfect vaccination, by comparing the spread rate of three types of mutant pathogens, in response to three types of vaccines. All mutant types spread faster in response to a transmission-blocking vaccine, relative to vaccines that reduce the proportion of exposed vaccinated individuals becoming infectious, and to vaccines that reduce the length of the infectious period; this difference increases with increasing vaccine efficacy. We interpret our results using the first published Price equation formulation for an SEIR model, and find that our main result is explained by the effects of vaccines on the equilibrium host distribution across epidemiological classes. In particular, the proportion of vaccinated infectious individuals among all exposed and infectious hosts, which is relatively higher in the transmission-blocking vaccine scenario, is important in explaining the faster spread of mutant strains in response to that vaccine. Our work illustrates the connection between epidemiological and evolutionary dynamics, and the need to incorporate both in order to explain and interpret findings of complicated infectious disease dynamics.


Evolutionary epidemiology Vaccination Resistance  Price equation Influenza SEIR 

Mathematics Subject Classification (2000)

34-XX 37N25 92B05 

Supplementary material

285_2013_654_MOESM1_ESM.pdf (144 kb)
Supplementary material 1 (pdf 144 KB)

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Odum School of EcologyUniversity of GeorgiaAthensUSA
  2. 2.School of Forestry and Wildlife SciencesAuburn UniversityAuburnUSA
  3. 3.Department of Infectious Diseases, College of Veterinary Medicine University of GeorgiaAthensUSA

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