Rocky Mountain Journal of Mathematics

Waning Herd Immunity: A Challenge for Eradication of Measles

Seyed M. Moghadas, Murray E. Alexander, and Beni M. Sahai

Full-text: Open access

Article information

Rocky Mountain J. Math., Volume 38, Number 5 (2008), 1587-1607.

First available in Project Euclid: 22 September 2008

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Adaptive dynamics herd immunity vaccination epidemic patterns


Moghadas, Seyed M.; Alexander, Murray E.; Sahai, Beni M. Waning Herd Immunity: A Challenge for Eradication of Measles. Rocky Mountain J. Math. 38 (2008), no. 5, 1587--1607. doi:10.1216/RMJ-2008-38-5-1587.

Export citation


  • R. Águas, G. Gonçalves, and M.G.M. Gomes, Pertussis: Increasing disease as a consequence of reducing transmission, Lancet Infect. Dis. 6 (2006), 112-117.
  • M.E. Alexander, S.M. Moghadas, P. Rohani, and A.R. Summers, Modelling the effect of a booster vaccination on disease epidemiology, J. Math. Biol. 52 (2006), 290-306.
  • R.M. Anderson and R.M. May, Infectious diseases of humans, Oxford University Press, London, 1991.
  • D. Bin, C. Qichang, W. Ting, G. Chengyin, W. Xingzi, F. Hanhua and X. Yongzhong, Duration of immunity following immunization with live measles vaccine: 15 years of observation in Zhejiang province, China, Bulletin World Health Organization 69 (1991), 415-423.
  • R.C. Brunham, B. Pourbohloul, S. Mak, R. White and M.L. Rekart, The unexpected impact of a Chlamydia trachomatis infection control program on susceptibility to reinfection, J. Infectious Diseases 192 (2005), 1836-1844.
  • R.T. Chen, R. Weierbach, Z. Bisoffi, F. Cutts, P. Rhodes, S. Ramaroson, C. Ntembagara and F. Bizimana, A `post-honeymoon period' measles outbreak in Muyinga Sector Burundi, Int. J. Epidemiology 23 (1994), 185-193.
  • T. Cherian, A. Joseph and T.J. John, Low antibody response in infants with measles and children with subclinical measles virus infection, J. Trop. Med. Hyg. 87 (1984), 27-31.
  • C.J. Clements, M. Strassburg, F.T. Cutts and C. Torel, The epidemiology of measles, World Health Statist. Quart. 45 (1992), 285-291.
  • F.T. Cutts and L.E. Markowitz, Successes and failures in measles control, J. Infectious Diseases 170 (suppl 1), (1994), S32-41.
  • J. Dushoff, J.B. Plotkin, S.A. Levin and D.J.D. Earn, Dynamical resonance can account for seasonality of influenza epidemics, PNAS 101 (2004), 16915-16916.
  • D.J.D. Earn, P. Rohani, B.M. Bolker and B.T. Grenfell, A simple model for complex dynamical transitions in epidemics, Science 287 (2000), 667-670.
  • P.E.M. Fine, Herd immunity: History, theory, practice, Epidemiologic Review 15 (1993), 265-301.
  • R. Gani and S. Leach, Transmission potential of smallpox in contemporary populations, Nature 414 (2001), 748-751.
  • M.A. Garly and P. Aaby, The challenge of improving the efficacy of measles vaccine, Acta Tropica 85 (2003), 1-17.
  • K. Glass and B.T. Grenfell, Antibody dynamics in childhood diseases: waning and boosting of immunity and the impact of vaccination, J. Theoret. Biol. 221 (2003), 121-131.
  • --------, Waning immunity and subclinical measles infection in England, Vaccine 22 (2004), 4110-4116.
  • S. Gupta, R.W. Snow, C.A. Donnelly, K. Marsh and C. Newbold, Immunity to non-cerebral severe malaria is acquired after one or two infections, Nature Med. 5 (1999), 340-343.
  • T.L. Gustafson, A.W. Lievens, P.A. Brunell, R.G. Moellenberg, C.M. Buttery and L.M. Sehulster, Measles outbreak in a fully immunized secondary school population, New England J. Medicine 316 (1987), 771-774.
  • H.W. Hethcote, The mathematics of infectious diseases, SIAM Rev. 42 (2002), 599-653.
  • T.B. Hyde, G.H. Dayan, J.R. Langidrik, R. Nandy, R. Edwards, K. Briand, M. Konelios, M. Marin, H.Q. Nguyen, A.P. Khalifah, M.J. O'Leary, N.J. Williams, W.J. Bellini, D. Bi, C.J. Brown, J.F. Seward and M.J. Papania, Measles outbreak in the Republic of the Marshall Islands, Internat. J. Epidemiology 35 (2006), 299-306.
  • W. Janaszek, N.J. Gay and W. Gut, Measles vaccine efficacy during an epidemic in $1998$ in the highly vaccinated population in Poland, Vaccine 21 (2003), 473-478.
  • W. Janaszek and J. Slusarczyk, Immunity against measles in populations of women and infants in Poland, Vaccine 21, 2948-2953.
  • M.J. Keeling and B.T. Grenfell, Understanding the persistence of measles: Reconciling theory, simulation and observation, Proc. R. Soc. Lond. 269 (2002), 335-343.
  • P.H. Lambert, M. Liu and C.A. Siegrist, Can successful vaccines teach us how to induce efficient protective immune responses?, Nature Med. 11 (2005), S54-S62.
  • A.R. McLean, After the honeymoon in measles control, The Lancet 345 (1995), 272.
  • R. Miralles, P.J. Gerrish, A. Moya and S.F. Elena, Clonal interference and the evolution of RNA viruses, Science 285 (1999), 1745-1747.
  • S.M. Moghadas, Modelling the effect of imperfect vaccines on disease epidemiology, Discrete Continuous Dynam. Syst. 4 (2004), 999-1012.
  • W.J. Moss and F.P. Polack, Immune response to measles and measles vaccine: Challenges for measles control, Viral Immunology 14 (2001), 297-309.
  • J. Mossong and C.P. Muller, Modelling measles re-emergence as a result of waning of immunity in vaccinated population, Vaccine 21 (2003), 4597-4603.
  • J. Mossong, J. Nokes, D.J. Edmunds, W.J. Cox, M.J. Ratman and C.P. Muller, Modelling the impact of subclinical measles transmission in vaccinated populations with waning immunity, Amer. J. Epidemiology 150 (1999), 1238-1249.
  • J. Mossong, C.J. O'Callaghan and S. Ratnam, Modelling antibody response to measles vaccine and subsequent waning of immunity in a low exposure population, Vaccine 19 (2001), 523-529.
  • K. Parke, Epidemiology of communicable diseases, in Parke's textbook of preventive and social medicine, 15th edition, Jabalpur, %M/s Banarsidas Bhanoot, 1997.%pp. 118-120.
  • P. Rohani, D.J.D. Earn and B.T. Grenfell, Impact of vaccination on pertussis transmission in England and Wales, Lancet 355 (2000), 285-286.
  • M.H. Schierup, C.H. Mordhorst, C.P. Muller and L.S. Christensen, Evidence of recombination among early-vaccination era measles virus strain, BMC Evol. Biol. 5 (2005), 1-8.
  • R.W. Snow, J.A. Omumbo, B. Lowe, C.S. Molyneux, J.O. Obiero, A. Palmer, M.W. Weber, M. Pinder, B. Nahlen, C. Obonyo, C. Newbold, S. Gupta and K. Marsh, Relation between severe malaria morbidity in children and level of Plasmodium falciparum transmission in Africa, Lancet 349 (1997), 1650-1654.
  • P.M. Strebel and S.L. Cochi, Waving goodbye to measles, Nature 414 (2001), 695-696.
  • H.C. Whittle, P. Aaby, B. Samb, H. Jensen, J. Bennet and F. Simondon, Effect of subclinical infection on maintaining immunity against measles in vaccinatied children in West Africa, Lancet 353 (1999), 98-102.
  • R.M. Zinkernagel, On natural and artificial vaccination, Annual Review Immunol. 21 (2003), 515-546.