Modelling the effect of a booster vaccination on disease epidemiology

Journal of Mathematical Biology

Volumn 52, Issue 3, 2006, Pages 290-306

  Alexander, M E ^a   Moghadas, S M ^a   Rohani, P ^b   Summers, A R ^a  

^a NATIONAL RESEARCH COUNCIL CANADA   (Canada)

^b UNIVERSITY OF GEORGIA   (United States)

Author keywords

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

Indexed keywords

ALGORITHM; BIOLOGICAL MODEL; COMMUNICABLE DISEASE; COMPUTER SIMULATION; EPIDEMIC; HUMAN; IMMUNIZATION; IMMUNOLOGY; MASS IMMUNIZATION; MEASLES; PERIODICITY; REVIEW; VACCINATION;

ALGORITHMS; COMMUNICABLE DISEASES; COMPUTER SIMULATION; DISEASE OUTBREAKS; HUMANS; IMMUNIZATION, SECONDARY; MASS IMMUNIZATION; MEASLES; MODELS, BIOLOGICAL; PERIODICITY; VACCINATION;

EID: 32544433313     PISSN: 03036812     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00285-005-0356-0     Document Type: Review

References (50)

1. Anderson, R.M., Grenfell, B.T.: Quantitative investigations of different vaccination policies for the control of congentila rubella syndrome (CRS) in the United Kingdom. J. Hyg. Camb. 96, 305-333 (1986)
2. Anderson, R.M., May, R.M.: Infectious Diseases of Humans. Oxford Univ. Press, London/New York, 1991
3. Behrman, R.E., Kliegman, R.M.: Nelson Essentials of Paediatrics. Saunders, 1998
4. Breban, R., Blower, S., Geffen, D.: Letter to the Editor: The reinfection threshold does not exist. J. Theor. Biol. 235, 151-152 (2005)
5. Bolker, B.M.: Chaos and complexity in measles models: a comparative numerical study. IMA J. Math. Appl. Med. Biol. 10, 83-95 (1993)
6. Böttiger, M., Forsgren, M.: Twenty years' experience of rubbela vaccination in Sweden: 10 years of selective vaccination (of 12-year-old girls and of women postpartum) and 13 years of a general two-dose vaccination. Vaccine 15, 1538-1544 (1997)
7. Chen, R.T., Markowitz, L.E., Albrecht, P.: Measles antibodies: re-evaluation of protective titres. J. Infect. Dis. 162, 1036-1062 (1990)
8. de Francisco, A., Hall, A.J., Unicomb, L., Chakraborty, J., Yunus, M., Sack, R.B.: Maternal measles antibody decay in rural Bangladeshi infants-implications for vaccination schedules. Vaccine 16, 564-568 (1998)
9. Dietz, K.: The evaluation of rubella vaccination strategies. The Mathematical Theory of the Dynamics of Biological population II. (Academic Press, NY, NY 1981) 81-98
10. Davidkin, I., Valle, M.: Vaccine-induced measles virus antibodies after two doses of combined measles, mumps and rubella vaccine: a 12-year follow-up in two cohorts. Vaccine 16, 2052-2057 (1998)
11. Earn, D.J.D., Rohani, P., Bolker, B.M., Grenfell, B.T.: A simple model for complex dynamical transitions in epidemics. Science 287, 667-670 (2000)
12. Fenner, F., Henderson, D.A., Arita, I., Jezek, Z., Ladnyi, I.D.: Smallpox and its eradication. WHO, 1998
13. Garly, M.A., Aaby, P.: The challenge of improving the efficacy of measles vaccine. Acta Tropica 85, 1-17 (2003)
14. Gomes, M.G.M., White, L.J., Medley, G.F.: Infection, reinfection, and vaccination under suboptimal immune protection: epidemiological perspectives. J. Theor. Biol. 228, 539-549 (2004)
15. Gomes, M.G.M., White, L.J., Medley, G.F.: The reinfection threshold. J. Theor. Biol. 236, 111-113 (2005)
16. Gustavson, T.L., Lievens, A.W., Brunell, P.A.: Measles outbreak in a fully immunized secondary school population. 316, 771-774 (1987)
17. Galazka, A.M., Robertson, S.E., Oblapenko, G.P.: Resurgence of diphteria. Eur. J. Epidemiol. 11, 95-105 (1995)
18. Gay, N.J., Pelletier, L., Duclos, P.: Modelling the incidence of measles in Canada: an assessment of the options for vaccination policy. Vaccine 16, 794-801 (1998)
19. Guckenheimer, J., Holmes, P.: Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields, AMS 42, Springer-Verlag, New York, Inc. 1983
20. Henao-Restrepo, A-M., Strebel, P., Hoekstra, E.J., Birmingham, M., Bilous, J.: Experience in global measles control, 1990-2000. J. Infec. Dis. 187, S15-21 (2003)
21. Hethcote, H.W.: The mathematics of infectious diseases. SIAM Rev. 42 (4), 599-653 (2000)
22. Janaszek, W., Gay, N.J., Gut, W.: Measles vaccine efficacy during an epidemic in 1998 in the highly vaccinated population in Poland. Vaccine 21, 473-478 (2003)
23. Janaszek, W., Slusarczyk, J.: Immunity against measles in population of women and infants in Poland. Vaccine 21, 2948-2953 (2003)
24. Katzmann, W., Dietz, K.: Evaluation of age-specific vaccination strategies. Theor. Pop. Biol. 25, 125-137 (1984)
25. Keeling, M.J., Grenfell, B.T.: Understanding the persistence of measles: reconciling theory, simulation and observation. Proc. R. Soc. Lond. B 269, 335-343 (2002)
26. Keeling, M.J., Rohani, P., Grenfell, B.T.: Seasonally forced disease dynamics explored as switching between attractors. Phys. D 148, 317-335 (2001)
27. Kribs-Zaleta, C.M., Martcheva, M.: Vaccination strategies and backward bifurcation in an age-since-infection structured model. Math. Biosci. 177, 317-332 (2002)
28. Kribs-Zaleta, C.M., Velasco-Hernández, J.X.: A simple vaccination model with multiple endemic states. Math. Biosci. 164, 183-201 (2000)
29. Lakshmikantham, V., Leela, S.: Differential and Integral Inequalities: Theory and Applications. Academic Press, New York, 1969.
30. Li, X-Z., Gupur, G.: Global stability of an age-structured SIRS epidemic model with vaccination. Discrete Contin. Dyn. Syst. Ser. B, 4, 643-652 (2004)
31. McLean, A.R., Anderson, R.M.: Measles in developing countries. Part I. Epidemiological parameters and patterns. Epidemiol. Infect. 100, 11-133 (1988)
32. Moghadas, S.M.: Modelling the effect of imperfect vaccines on disease epidemiology. Discrete Contin. Dyn. Syst. Ser. B, 4, 999-1012 (2004)
33. Moghadas, S.M., Gumel, A.B.: A mathematical study of a model for childhood diseases with non-permanent immunity. J. Comput. Appl. Math. 157, 347-363 (2003)
34. Mossong, J., Muller, C.P.: Modelling measles re-emergence as a result of waning of immunity in vaccinated population. Vaccine, 21, 4597-4603 (2003)
35. Mossong, J., Nokes, J., Edmunds, D.J., Cox, W.J., Ratman, M.J., Muller, C.P.: Modelling the impact of subclinical measles transmission in vaccinated populations with waning immunity. Am. J. Epidemiol. 150, 1238-1249 (1999)
36. Müller, J.: Optimal vaccination patterns in age-structured populations. SIAM J. Appl. Math. 59, 222-241 (1998)
37. Paulo, A.C., Gomes, M.C., Casinhas, A.C., Horta, A.: Multiple dose vaccination against childhood diseases: high coverage with the first dose remains crucial for eradication. IMA J. Math. Appl. Med. Biol. 17, 201-212 (2000)
38. Pelletier, L., Chung, P., Duclos, P., Manga, P., Scott, J.: A benefit-cost analysis of two-dose measles immunization in Canada. Vaccine 16, 989-996 (1998)
39. Piccardi, C., Lazzaris, S.: Vaccination policies for chaos reduction in childhood epidemics. IEEE Trans. Biomed. Eng. 45, 591-595 (1998)
40. Piyawong, W., Twizell, E.H., Gumel, A.B.: An unconditionally convergent finite-difference scheme for the SIR model. Appl. Math. Comput. 146, 611-625 (2003)
41. Ratnam, S., West, R., Gadag, V., Burris, J.: Measles immunization strategy: measles antibody response following MMR II vaccination of children at one year of age. Can. J. Public Health 87, 97-100 (1996)
42. Rohani, P., Earn, D.J.D., Finkenstädt, B., Grenfell, B.T.: Population dynamics interference among childhood diseases. Proc. R. Soc. Lond. B 265, 2033-2041 (1998)
43. Rohani, P., Kelling, M.J., Grenfell, B.T.: The interplay between determinism and stochasticity in childhood diseases. Am. Nat. 159, 469-481 (2002)
44. Rouderfer, V., Becker, N.G., Hethcote, H.W.: Waning immunity and its effect on vaccination schedules. Math. Biosci. 124, 59-82 (1994)
45. Shulgin, B., Stone, L., Agur, A.: Pulse vaccination strategy in the SIR epidemic model. Bull. Math. Biol. 60, 1123-1148 (1998)
46. Strebel, P., Cochi, S., Grabowsky, M., Bilous, J., Hersh, B.S., Okwo-Bele, J.M., Hoekstra, E., Wright, P., Katz, S.: The unfinished measles immunization agenda. J. Inf. Dis. 187, S1-S7 (2003)
47. Teitelbaum, M.A., Edmunds, M.: Immunization and vaccine-preventable illness, United States, 1992-1997. Stat. Bull. Metrop. Insur. Co. 80, 13-20 (1999)
48. Whittle, H.C., Aaby, P., Samb, B., Jensen, H., Bennet, J., Simondon, F.: Effect of subclinical infection on maintaining immunity against measles in vaccinated children in West Africa. Lancet 353, 98-102 (1999)
49. Williams, B.G., Cutts, F.T., Dye, C.: Measles vaccination policy. Epidemiol. Infect. 115, 603-621 (1995)
50. Wright, S.W.: Pertussis infection in adults. South. Med. J. 91, 702-708 (1998)