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The evolutionary consequences of alternative types of imperfect vaccines

Journal of Mathematical Biology volume 68, pages 969–987 (2014)Cite this article

Abstract

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.

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References

  • Bloom J, Gong L, Baltimore D (2010) Permissive secondary mutations enable the evolution of influenza oseltamivir resistance. Science 328(5983):1272–1275. doi:10.1126/science.1187816

    Article  Google Scholar 

  • Dancer SJ (2011) Hospital cleaning in the 21st century. Eur J Clin Microbiol Infect Dis 30(12):1473–1481. doi:10.1007/s10096-011-1250-x

    Article  Google Scholar 

  • Day T, Gandon S (2006) Insights from Price’s equation into evolutionary epidemiology. DIMACS Ser Discrete Math Theor Comput Sci 71:23–44

    MathSciNet  Google Scholar 

  • Day T, Gandon S (2012) The evolutionary epidemiology of multilocus drug resistance. Evolution 66(5):1582–1597. doi:10.1111/j.1558-5646.2011.01533.x

    Article  Google Scholar 

  • Day T, Proulx SR (2004) A general theory for the evolutionary dynamics of virulence. American Naturalist 163(4):E40–E63. doi:10.1086/382548

    Article  Google Scholar 

  • De Clercq E (2004) Antiviral drugs in current clinical use. J Clin Vir 30(2):115–133. doi:10.1016/j.jcv.2004.02.009

    Article  Google Scholar 

  • Diekmann O, Heesterbeek J, Metz J (1990) On the definition and the computation of the basic reproductive ratio R0 in models for infectious diseases in heterogeneous populations. J Math Biol 28(4):365–382

    Article  MATH  MathSciNet  Google Scholar 

  • Fryer HR, McLean AR (2011) Modelling the spread of HIV immune escape mutants in a vaccinated population. PLoS Comput Biol 7(12):e1002,289. doi:10.1371/journal.pcbi.1002289

  • Gandon S, Day T (2007) The evolutionary epidemiology of vaccination. J Roy Soc Interface 4(16):803–817. doi:10.1098/rsif.2006.0207

    Article  Google Scholar 

  • Gandon S, Day T (2008) Evidences of parasite evolution after vaccination. Vaccine 26:C4–C7. doi:10.1016/j.vaccine.2008.02.007

    Article  Google Scholar 

  • Gandon S, Mackinnon MJ, Nee S, Read AF (2001) Imperfect vaccines and the evolution of pathogen virulence. Nature 414(6865):751–756. doi:10.1038/414751a

    Article  Google Scholar 

  • Gupta S, Ferguson N, Anderson R (1997) Vaccination and the population structure of antigenically diverse pathogens that exchange genetic material. Proc R Soc Lond Ser B-Biol Sci 264(1387):1435–1443

    Article  Google Scholar 

  • Holmes EC (2009) The evolution and emergence of RNA viruses. Oxford University Press, Oxford

    Google Scholar 

  • Keeling MJ, Rohani P (2007) Modeling Infectious Diseases in Humans and Animals, 2007th edn. Princeton University Press, Princeton

    Google Scholar 

  • Kramarz P, Monnet D, Nicoll A, Yilmaz C, Ciancio B (2009) Use of oseltamivir in 12 European countries between 2002 and 2007-lack of association with the appearance of oseltamivir-resistant influenza A(H1N1) viruses. Euro Surveill 14(5)

  • Martcheva M, Bolker BM, Holt RD (2008) Vaccine-induced pathogen strain replacement: what are the mechanisms? J Roy Soc Interface 5(18):3–13. doi:10.1098/rsif.2007.0236

    Google Scholar 

  • McLean A (1995) Vaccination, evolution and changes in the efficacy of vaccines—a theoretical framework. Proc R Soc Lond Ser B-Biol Sci 261(1362):389–393. doi:10.1098/rspb.1995.0164

    Article  Google Scholar 

  • McLean A (1998) Vaccines and their impact on the control of disease. Br Med Bull 54(3):545–556

    Article  Google Scholar 

  • Park A, Daly J, Lewis N, Smith D, Wood J, Grenfell B (2009) Quantifying the impact of immune escape on transmission dynamics of influenza. Science 326(5953):726–728. doi:10.1126/science.1175980

    Article  Google Scholar 

  • Presanis AM, De Angelis D, Hagy A, Reed C, Riley S, Cooper BS, Finelli L, Biedrzycki P, Lipsitch M, New York City Swine Flu Investigation Team (2009) The severity of pandemic H1N1 influenza in the United States, from April to July 2009: a Bayesian analysis. PLoS Med 6(12):e1000,207. doi:10.1371/journal.pmed.1000207

  • Price G (1970) Selection and covariance. Nature 227(5257):520. doi:10.1038/227520a0

    Article  Google Scholar 

  • Regoes RR, Bonhoeffer S (2006) Emergence of drug-resistant influenza virus: population dynamical considerations. Science 312(5772):389–391. doi:10.1126/science.1122947

    Article  Google Scholar 

  • Restif O (2009) Evolutionary epidemiology 20 years on: challenges and prospects. Infect Genet Evol 9(1):108–123. doi:10.1016/j.meegid.2008.09.007

    Article  Google Scholar 

  • Restif O, Grenfell BT (2007) Vaccination and the dynamics of immune evasion. J Roy Soc Interface 4(12):143–153. doi:10.1098/rsif.2006.0167

    Article  Google Scholar 

  • Russell CA, Jones TC, Barr IG, Cox NJ, Garten RJ, Gregory V, Gust ID, Hampson AW, Hay AJ, Hurt AC, de Jong JC, Kelso A, Klimov AI, Kageyama T, Komadina N, Lapedes AS, Lin YP, Mosterin A, Obuchi M, Odagiri T, Osterhaus AD, Rimmelzwaan GF, Shaw MW, Skepner E, Stohr K, Tashiro M, Fouchier RA, Smith DJ (2008) Influenza vaccine strain selection and recent studies on the global migration of seasonal influenza viruses. Vaccine 26(Supplement 4):D31–D34. doi:10.1016/j.vaccine.2008.07.078

    Article  Google Scholar 

  • Saleh S, Haddadin RNS, Baillie S, Collier PJ (2011) Triclosan—an update. Lett Appl Microbiol 52(2):87–95. doi:10.1111/j.1472-765X.2010.02976.x

    Article  Google Scholar 

  • Sanjuan R, Nebot MR, Chirico N, Mansky LM, Belshaw R (2010) Viral mutation rates. J Virol 84(19):9733–9748. doi:10.1128/JVI.00694-10

    Article  Google Scholar 

  • Satou K, Nishiura H (2006) Basic reproduction number for equine-2 influenza virus a (H3N8) epidemic in racehorse facilities in Japan, 1971. J Equine Vet Res 26(7):310–316. doi:10.1016/j.jevs.2006.05.003

    Article  Google Scholar 

  • Stilianakis NI, Perelson AS, Hayden FG (1998) Emergence of drug resistance during an influenza epidemic: insights from a mathematical model. J Infect Dis 177(4):863–873

    Article  Google Scholar 

  • Taubenberger J (2006) The origin and virulence of the 1918 “Spanish” influenza virus. Proc Am Phil Soc 150(1):86–112

    Google Scholar 

  • Thompson M, Shay D, Zhou H, Bridges C, Cheng P, Burns E, Bresee J, Cox N (2010) Estimates of deaths associated with seasonal influenza-United States, 1976–2007 (Reprinted from MMWR, vol 59, pp 1057–1062, 2010). JAMA-J Am Med Assoc 304(16):1778–1780

    Google Scholar 

  • Webby R, Webster R (2003) Are we ready for pandemic influenza? Science 302(5650):1519–1522

    Article  Google Scholar 

  • Wei C, Boyington J, McTamney P, Kong W, Pearce M, Xu L, Andersen H, Rao S, Tumpey T, Yang Z, Nabel G (2010) Induction of broadly neutralizing H1N1 influenza antibodies by vaccination. Science 329(5995):1060–1064. doi:10.1126/science.1192517

    Article  Google Scholar 

  • Williams PD (2010) Darwinian interventions: taming pathogens through evolutionary ecology. Trends Parasitol 26(2):83–92. doi:10.1016/j.pt.2009.11.009

    Article  Google Scholar 

  • Yasui K, Amano Y, Minami I, Nakamura S, Akazawa Y, Uchida N (2007) Recent changes in the trends of seasonal influenza outbreaks in the Nagano prefectural area of Japan: an oseltamivir effect? J Infect Chemother 13(6):429–431. doi:10.1007/s10156-007-0554-3

    Article  Google Scholar 

  • zur Wiesch PA, Kouyos R, Engelstädter J, Regoes RR, Bonhoeffer S (2011) Population biological principles of drug-resistance evolution in infectious diseases. Lancet Infec Dis 11(3):236–247. doi:10.1016/S1473-3099(10)70264-4

    Article  Google Scholar 

Download references

Acknowledgments

This work has been funded by the University of Georgia and the McDonnell Foundation. We thank the valuable contributions of John Drake, Richard Hall, John Paul Schmidt, Andreas Handel, Andrew Kramer, Sean P. Maher, James Haven, Suzanne O’Regan and other members of the Computational Ecology and Epidemiology Study Group at the Odum School of Ecology at the University of Georgia.

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  1. Krisztian Magori

    Present address: School of Forestry and Wildlife Sciences, Auburn University, Auburn, USA

Affiliations

  1. Odum School of Ecology, University of Georgia, Athens, GA, USA

    Krisztian Magori & Andrew W. Park

  2. Department of Infectious Diseases, College of Veterinary Medicine, University of Georgia, Athens, USA

    Andrew W. Park

Authors
  1. Krisztian Magori
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  2. Andrew W. Park
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Correspondence to Krisztian Magori.

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Magori, K., Park, A.W. The evolutionary consequences of alternative types of imperfect vaccines. J. Math. Biol. 68, 969–987 (2014). https://doi.org/10.1007/s00285-013-0654-x

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  • DOI: https://doi.org/10.1007/s00285-013-0654-x

Keywords

  • Evolutionary epidemiology
  • Vaccination
  • Resistance
  • Price equation
  • Influenza
  • SEIR

Mathematics Subject Classification (2000)

  • 34-XX
  • 37N25
  • 92B05