Modelling the long-term dynamics of pre-vaccination pertussis

Journal of the Royal Society Interface

Volumn 9, Issue 76, 2012, Pages 2959-2970

  Rozhnova, Ganna ^a,b   Nunes, Ana ^a  

^a Centro de Fisica da Materia Condensada   (Portugal)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Childhood infections; Pertussis; Power spectra; Recurrent epidemics; Stochastic fluctuations

Indexed keywords

DYNAMICS; POWER SPECTRUM; STOCHASTIC SYSTEMS; VACCINES;

CHILDHOOD INFECTIONS; PERTUSSIS; POWER-SPECTRA; RECURRENT EPIDEMICS; STOCHASTIC FLUCTUATION;

STOCHASTIC MODELS;

ADAPTIVE IMMUNITY; ARTICLE; DYNAMICS; IMMUNE RESPONSE; PERTUSSIS; POWER SPECTRUM; QUALITATIVE ANALYSIS; QUANTITATIVE ANALYSIS; REINFECTION; SIMULATION; STOCHASTIC MODEL; VACCINATION;

EID: 84866940158     PISSN: 17425689     EISSN: 17425662     Source Type: Journal    
DOI: 10.1098/rsif.2012.0432     Document Type: Article

References (52)

1. Trottier, H., Philippe, P. & Roy, R. 2006 Stochastic modeling of empirical time series of childhood infectious diseases data before and after mass vaccination. Emerg. Themes Epidemiol. 3, 9. (doi:10.1186/1742-7622-3-9)
2. Yorke, J. A. & London, W. P. 1973 Recurrent outbreaks of measles, chickenpox and mumps. II. Systematic differences in contact rates and stochastic effects. Am. J. Epidemiol. 98, 469-482.
3. Wallinga, J., Lévy-Bruhl, D., Gay, N. J. & Wachmann, C. H. 2001 Estimation of measles reproduction ratios and prospects for elimination of measles by vaccination in some Western European countries. Epidemiol. Infect. 127, 281-295. (doi:10.1017/S095026880100601X)
4. Broutin, H., Guégan, J. F., Elguero, E., Simondon, F. & Cazelles, B. 2005 Large-scale comparative analysis of pertussis population dynamics: periodicity, synchrony, and impact of vaccination. Am. J. Epidemiol. 161, 1159-1167. (doi:10.1093/aje/kwi141)
5. Broutin, H., Mantilla-Beniers, N. B., Simondon, F., Aaby, P., Grenfell, B. T., Guégan, J. F. & Rohani, P. 2005 Epidemiological impact of vaccination on the dynamics of two childhood diseases in rural Senegal. Microbes Infect. 7, 593-599. (doi:10.1016/j.micinf.2004.12.018)
6. Centers for Disease Control and Prevention. 2002 Pertussis: United States, 1997-2000. Morb. Mortal Wkly Rep. 51, 73-76.
7. Skowronski, D. M., De Serres, G., MacDonald, D., Wu, W., Shaw, C., Macnabb, J., Champagne, S., Patrick, D. M. & Halperin, S. A. 2002 The changing age and seasonal profile of pertussis in Canada. J. Infect. Dis. 185, 1448-1453. (doi:10.1086/340280)
8. de Melker, H. E., Schellekens, J. F., Neppelenbroek, S. E., Mooi, F. R., Rümke, H. C. & Conyn-van Spaendonck, M. A. 2000 Reemergence of pertussis in the highly vaccinated population of the Netherlands: observations on surveillance data. Emerg. Infect. Dis. 6, 348-357. (doi:10.3201/eid0604. 000404)
9. Crowcroft, N. S. & Pebody, R. G. 2006 Recent developments in pertussis. Lancet 367, 1926-1936. (doi:10.1016/S0140-6736(06)68848-X)
10. Lavine, J. S., King, A. A. & Bjørnstad, O. N. 2011 Natural immune boosting in pertussis dynamics and the potential for long-term vaccine failure. Proc. Natl Acad. Sci. USA 108, 7259-7264. (doi:10.1073/pnas.1014394108)
11. Soper, H. 1929 The interpretation of periodicity in disease prevalence. J. R. Stat. Soc. 92, 34-73. (doi:10.2307/2341437)
12. London, W. P. & Yorke, J. A. 1973 Recurrent outbreaks of measles, chickenpox and mumps. I. Seasonal variation in contact rates. Am. J. Epidemiol. 98, 453-468.
13. Fine, P. E. & Clarkson, J. A. 1982 Measles in England and Wales - I: an analysis of factors underlying seasonal patterns. Int. J. Epidemiol. 11, 5-14. (doi:10.1093/ije/11.1.5)
14. Fine, P. E. & Clarkson, J. A. 1986 Seasonal influences on pertussis. Int. J. Epidemiol. 15, 237-247. (doi:10.1093/ije/15.2.237)
15. Grenfell, B. T., Bjørnstad, O. N. & Kappey, J. 2001 Travelling waves and spatial hierarchies in measles epidemics. Nature 414, 716-723. (doi:10.1038/414716a)
16. Earn, D. J. D., Rohani, P., Bolker, B. M. & Grenfell, B. T. 2000 A simple model for complex dynamical transitions in epidemics. Science 287, 667-670. (doi:10.1126/science.287.5453.667)
17. Bauch, C. T. & Earn, D. J. D. 2003 Transients and attractors in epidemics. Proc. R. Soc. Lond. B 270, 1573-1578. (doi:10.1098/rspb.2003.2410)
18. Keeling, M. J., Rohani, P. & Grenfell, B. T. 2001 Seasonally forced disease dynamics explored as switching between attractors. Physica D 148, 317-335. (doi:10.1016/S0167-2789(00)00187-1)
19. Wearing, H. J., Rohani, P. & Keeling, M. J. 2005 Appropriate modeling of infectious diseases. PLoS Med. 2, e239. (doi:10.1371/journal.pmed.0020239)
20. Simões, M., Telo da Gama, M. M. & Nunes, A. 2008 Stochastic fluctuations in epidemics on networks. J. R. Soc. Interface 5, 555-566. (doi:10.1098/rsif.2007.1206)
21. Edmunds, W. J., Kafatos, G., Wallinga, J. & Mossong, J. R. 2006 Mixing patterns and the spread of close-contact infectious diseases. Emerg. Themes Epidemiol. 3, 10. (doi:10.1186/1742-7622-3-10)
22. Read, J. M., Eames, K. T. & Edmunds, W. J. 2008 Dynamic social networks and the implications for the spread of infectious disease. J. R. Soc. Interface 5, 1001-1007. (doi:10.1098/rsif.2008.0013)
23. Hethcote, H. W. 1997 An age-structured model for pertussis transmission. Math. Biosci. 145, 89-136. (doi:10.1016/S0025-5564(97)00014-X)
24. Allen, L. J. & Driessche, P. 2006 Stochastic epidemic models with a backward bifurcation. Math. Biosci. Eng. 3, 445-458. (doi:10.3934/mbe.2006.3. 445)
25. Keeling, M. J. & Eames, K. T. 2005 Networks and epidemic models. J. R. Soc. Interface 2, 295-307. (doi:10.1098/rsif.2005.0051)
26. Alonso, D., McKane, A. J. & Pascual, M. 2007 Stochastic amplification in epidemics. J. R. Soc. Interface 4, 575-582. (doi:10.1098/rsif.2006.0192)
27. Rozhnova, G. & Nunes, A. 2009 Fluctuations and oscillations in a simple epidemic model. Phys. Rev. E 79, 041922. (doi:10.1103/PhysRevE.79.041922)
28. Volz, E. & Meyers, L. A. 2009 Epidemic thresholds in dynamic contact networks. J. R. Soc. Interface 6, 233-241. (doi:10.1098/rsif.2008.0218)
29. Black, A. J., McKane, A. J., Nunes, A. & Parisi, A. 2009 Stochastic fluctuations in the susceptible-infective-recovered model with distributed infectious periods. Phys. Rev. E 80, 021922. (doi:10.1103/PhysRevE.80.021922)
30. Rozhnova, G. & Nunes, A. 2010 Stochastic effects in a seasonally forced epidemic model. Phys. Rev. E 82, 041906. (doi:10.1103/PhysRevE.82.041906)
31. Metcalf, C. J., Bjørnstad, O. N., Grenfell, B. T. & Andreasen, V. 2009 Seasonality and comparative dynamics of six childhood infections in pre-vaccination Copenhagen. Proc. R. Soc. B 276, 4111-4118. (doi:10.1098/rspb. 2009.1058)
32. Grassly, N. C. & Fraser, C. 2006 Seasonal infectious disease epidemiology. Proc. R. Soc. B 273, 2541-2550. (doi:10.1098/rspb.2006.3604)
33. Meyers, L. A., Pourbohloul, B., Newman, M. E., Skowronski, D. M. & Brunham, R. C. 2005 Network theory and SARS: predicting outbreak diversity. J. Theor. Biol. 232, 71-81. (doi:10.1016/j.jtbi.2004.07.026)
34. Eubank, S., Guclu, H., Kumar, V. S., Marathe, M. V., Srinivasan, A., Toroczkai, Z. & Wang, N. 2004 Modelling disease outbreaks in realistic urban social networks. Nature 429, 180-184. (doi:10.1038/nature02541)
35. Broutin, H., Viboud, C., Grenfell, B. T., Miller, M. A. & Rohani, P. 2010 Impact of vaccination and birth rate on the epidemiology of pertussis: a comparative study in 64 countries. Proc. R. Soc. B 277, 3239-3245. (doi:10.1098/rspb.2010.0994)
36. Rohani, P., Keeling, M. J. & Grenfell, B. T. 2002 The interplay between determinism and stochasticity in childhood diseases. Am. Nat. 159, 469-481. (doi:10.1086/339467)
37. Nguyen, H. T. & Rohani, P. 2008 Noise, nonlinearity and seasonality: the epidemics of whooping cough revisited. J. R. Soc. Interface 5, 403-413. (doi:10.1098/rsif.2007.1168)
38. Ferrari, M. J., Grais, R. F., Bharti, N., Conlan, A. J., Bjørnstad, O. N., Wolfson, L. J., Guerin, P. J., Djibo, A. & Grenfell, B. T. 2008 The dynamics of measles in sub-Saharan Africa. Nature 451, 679-684. (doi:10.1038/nature06509)
39. Mantilla-Beniers, N. B., Bjørnstad, O. N., Grenfell, B. T. & Rohani, P. 2010 Decreasing stochasticity through enhanced seasonality in measles epidemics. J. R. Soc. Interface 7, 727-739. (doi:10.1098/rsif.2009.0317)
40. Wearing, H. J. & Rohani, P. 2009 Estimating the duration of pertussis immunity using epidemiological signatures. PLoS Pathog. 5, e1000647. (doi:10.1371/journal.ppat.1000647)
41. Black, A. J. & McKane, A. J. 2010 Stochasticity in staged models of epidemics: quantifying the dynamics of whooping cough. J. R. Soc. Interface 7, 1219-1227. (doi:10.1098/rsif.2009.0514)
42. Rohani, P., Zhong, X. & King, A. A. 2010 Contact network structure explains the changing epidemiology of pertussis. Science 330, 982-985. (doi:10.1126/science.1194134)
43. Aguas, R., Gonalves, G. & Gomes, M. G. 2006 Pertussis: increasing disease as a consequence of reducing transmission. Lancet Infect. Dis. 6, 112-117. (doi:10.1016/S1473-3099(06)70384-X)
44. Gomes, M. G., White, L. J. & Medley, G. F. 2004 Infection, reinfection, and vaccination under suboptimal immune protection: epidemiological perspectives. J. Theor. Biol. 228, 539-549. (doi:10.1016/j.jtbi.2004.02.015)
45. Anderson, R. A. & May, R. M. 1991 Infectious diseases of humans. Oxford, UK: Oxford University Press.
46. Clarkson, J. A. & Fine, P. E. M. 1985 The efficiency of measles and pertussis notification in England and Wales. Int. J. Epidemiol. 14, 153-168. (doi:10.1093/ije/14.1.153)
47. Rohani, P., Earn, D. J. D. & Grenfell, B. T. 1999 Opposite patterns of synchrony in sympatric disease metapopulations. Science 286, 968-971. (doi:10.1126/science.286.5441.968)
48. Wendelboe, A. M., Van Rie, A., Salmaso, S. & Englund, J. A. 2005 Duration of immunity against pertussis after natural infection or vaccination. Pediatr. Infect. Dis. J. 24, S58-S61. (doi:10.1097/01.inf.0000160914.59160.41)
49. Gillespie, D. T. 1976 A general method for numerically simulating the stochastic time evolution of coupled chemical reactions. J. Comput. Phys. 22, 403-434. (doi:10.1016/0021-9991(76)90041-3)
50. Anderson, D. F. 2007 A modified next reaction method for simulating chemical systems with time dependent propensities and delays. J. Chem. Phys. 127, 214107. (doi:10.1063/1.2799998)
51. Lu, T., Volfson, D., Tsimring, L. & Hasty, J. 2004 Cellular growth and division in the Gillespie algorithm. Syst. Biol. 1, 121-128. (doi:10.1049/sb:20045016)
52. van Kampen, N. G. 1992 Stochastic processes in physics and chemistry. Amsterdam, The Netherlands: Elsevier.