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Spatial and Temporal Dynamics of Rubella in Peru, 1997–2006: Geographic Patterns, Age at Infection and Estimation of Transmissibility

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Book cover Mathematical and Statistical Estimation Approaches in Epidemiology

Abstract

Detailed studies on the spatial and temporal patterns of rubella transmission are scarce particularly in developing countries but could prove useful in improving epidemiological surveillance and intervention strategies such as vaccination. We use highly refined spatial, temporal and age-specific incidence data of Peru, a geographically diverse country, to quantify spatial-temporal patterns of incidence and transmissibility for rubella during the period 1997–2006. We estimate the basic reproduction number (R 0) based on the mean age at infection and the per capita birth rate of the population as well as the reproduction number (accounting for the fraction of the population effectively protected to infection) using the initial intrinsic growth rate of individual outbreaks and estimates of epidemiological parameters for rubella. A wavelet time series analysis is conducted to explore the periodicity of the rubella weekly time series, and the results of our analyses are compared to those carried out for time series of other childhood infectious diseases. We also identify the presence of a critical community size and quantify spatial heterogeneity across geographic regions through the use of Lorenz curves and their corresponding Gini indices. The underlying distributions of rubella outbreak attack rates and epidemic durations across Peru are characterized.

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References

  1. Benenson AS (1985) Control of Communicable Diseases of Man. vol. 8. 14th ed. American Public Health Association;

    Google Scholar 

  2. World Health Organization. Rubella and Congenital Rubella Syndrome (CRS);. http://www.who.int/immunization_monitoring/diseases/rubella/en/ (accessed on September 21, 2008).

  3. Pan American Health Organization (1998) Public Health Burden of Rubella and CRS; EPI Newsletter Volume XX, Number 4.

    Google Scholar 

  4. Atkinson W, Hamborsky J, McIntyre L, Wolfe S (2007) Centers for Disease Control and Prevention. Epidemiology and Prevention of Vaccine-Preventable Diseases. 10th ed. Washington DC: Public Health Foundation;

    Google Scholar 

  5. Gao L, Hethcote HW (2006) Simulations of rubella vaccination strategies in China. Mathematical Biosciences. 202(2):371–385.

    Article  MATH  MathSciNet  Google Scholar 

  6. Robertson SE, Featherstone DA, Gacica-Dobo M, Hersh BS (2003) Rubella and congenital rubella syndrome: global update. Pan American Journal of Public Health.14(5):306–315.

    Google Scholar 

  7. Knox EG (1980) Strategy for rubella vaccination. International Journal of Epidemiology 9(1):13–23.

    Article  Google Scholar 

  8. Dietz K (1981) The evaluation of rubella vaccination strategies. In: Hiorns W. Cooke D, eds. The Mathematical Theory of the Dynamics of Biological Populations. vol. 2. New York: Academic Press p. 81–97.

    Google Scholar 

  9. Anderson RM, May RM (1983) Vaccination against Rubella and Measles: Quantitative Investigations of Different Policies. The Journal of Hygiene 90(2):259–325.

    Article  Google Scholar 

  10. Hethcote HW (1983) Measles and Rubella in the United States. American Journal of Epidemiology 117(1):2–13.

    Google Scholar 

  11. Edmunds WJ, Gay NJ, Kretzschmar M, Pebody RG (2000) The pre-vaccination epidemiology of measles, mumps and rubella in Europe: Implications for modelling studies. Epidemiology and infection 125(3):635–650.

    Article  Google Scholar 

  12. Brisson M, Edmunds WJ. (2003) Economic evaluation of vaccination programs: the impact of herd-immunity. Medical Decision Making 23(1):76–82.

    Article  Google Scholar 

  13. Glasser J, Pistol A, Rafila A, Marin M. (2008) Designing interventions to ease an under-ascertained burden via mathematical modeling: Rubella and congenital rubella syndrome in Romania. (Manuscript)

    Google Scholar 

  14. Bolker BM, Grenfell BT (1995) Space, persistence and dynamics of measles epidemics. Philosophical Transactions of the Royal Society of London 348(1325):309–320.

    Article  Google Scholar 

  15. Rohani P, Earn DJ, Finkenstadt B, Grenfell BT (1998) Population dynamic interference among childhood diseases. Proceedings of the Royal Society B: Biological Sciences 265(1410):2033–2041.

    Article  Google Scholar 

  16. Grenfell BT, Bjornstad ON, Kappey J (2001) Travelling waves and spatial hierarchies in measles epidemics. Nature 414:716–723.

    Article  Google Scholar 

  17. Rohani P, Green CJ, Mantilla-Beniers NB, Grenfell BT (2003) Ecological interference between fatal diseases. Nature 422(6934):885–888.

    Article  Google Scholar 

  18. Ferrari MJ, Grais RF, Bharti N, Conlan AJK, Bjornstad ON, Wolfson LJ, et al. (2008) The dynamics of measles in sub-Saharan Africa. Nature 451(7179):679–684.

    Article  Google Scholar 

  19. Peru Instituto Nacional de Estadistica e Informatica; http://www.inei.gob.pe/ (Accessed 1 February 2008).

  20. Wikipedia. Provinces of Peru; http://en.wikipedia.org/wiki/Proveinces_of_Peru (Accessed 1 February 2008).

  21. Daubechies I (1992) Ten lectures on wavelets. SIAM

    Google Scholar 

  22. Torrence C, Compo G (1998) A practical guide to wavelet analysis. Bullein of the American Meteorological Society. 79(1):61–78.

    Article  Google Scholar 

  23. Maraun D, Kurths J (2004) Cross wavelet analysis: Significance testing and pitfalls. Nonlinear Processes in Geophysics. 11:505–514.

    Google Scholar 

  24. Cazelles B, Chavez M, Magny GC, Guégan JF, Hales S (2007) Time-dependent spectral analysis of epidemiological time-series with wavelets. Journal of the Royal Society Interface. 4(15):625–636.

    Article  Google Scholar 

  25. Grinsted A, Moore JC, Jevrejeva S. Software for Cross Wavelet and Wavelet Coherence; http://www.pol.ac.uk/home/research/waveletcoherence/ (accessed on October 6, 2008).

  26. Anderson RM, May RM (1991) Infectious Diseases of Humans: Dynamics and Control. Oxford: Oxford University Press

    Google Scholar 

  27. Diekmann O, Heesterbeek JAP (2000) Mathematical Epidemiology of Infectious Diseases: Model Building, Analysis and Interpretation. Wiley.

    Google Scholar 

  28. Broutin H, Mantilla-Beniers NB, Simondon F, Aaby P, Grenfell BT, Guegan JF, et al. (2005) Epidemiological impact of vaccination on the dynamics of two childhood diseases in rural Senegal. Microbes and Infection. 7(4):593–999.

    Google Scholar 

  29. Wallinga J, Lipsitch M (2007) How generation intervals shape the relationship between growth rates and reproductive numbers. Proceedings of the Royal Society B: Biological Sciences. 274(1609):599.

    Article  Google Scholar 

  30. Bjornstad ON, Finkenstadt BF, Grenfell BT (2002) Dynamics of measles epidemics: Estimating scaling of transmission rates using a time series SIR model. Ecological Monographs. 72(2):169–184.

    Google Scholar 

  31. Earn DJ, Rohani P, Bolker BM, Grenfell BT (2000) A simple model for complex dynamical transitions in epidemics. Science 287(5453):667–670.

    Article  Google Scholar 

  32. Lipsitch M, Cohen T, Cooper B, Robins JM, Ma S, James L, et al. (2003) Transmission dynamics and control of severe acute respiratory syndrome. Science 300(5627).

    Google Scholar 

  33. Chowell G, Nishiura H, Bettencourt LM (2007) Comparative estimation of the reproduction number for pandemic influenza from daily case notification data. Journal of The Royal Society Interface 4(12):155–166.

    Article  Google Scholar 

  34. Grenfell BT, Bjornstad ON, Kappey J (2001) Travelling waves and spatial hierarchies in measles epidemics. Nature 414:716–723.

    Article  Google Scholar 

  35. Grenfell BT, Keeling MJ (1997) Disease extinction and community size: Modeling the presistence of measles. Science 275(5296):65–67.

    Article  Google Scholar 

  36. Grenfell B, Harwood J (1997) (Meta)population dynamics of infectious diseases. TRENDS in Ecology and Evolution 12(10):395–399.

    Article  Google Scholar 

  37. Rhodes CJ, Anderson RM (1996) Power laws governing epidemics in isolated populations. Nature 381(6583):600–602.

    Article  Google Scholar 

  38. Keeling M, Grenfell B (1999) Stochastic dynamics and a power law for measles variability. Philosophical Transactions of the Royal Society of London. 354(1384):769–776.

    Article  Google Scholar 

  39. Lee WC (1997) Characterizing exposure-disease association in human populations using the Lorenz curve and Gini index. Statistics in Medicine 16(7):729–739.

    Article  Google Scholar 

  40. Woolhouse MEJ, Dye C, Etard JF, Smith T, et al. (1997) Heterogeneities in the transmission of infectious agents: Implications for the design of control programs. In: Proceedings of the National Academy of Sciences of the United States of America. vol. 94;p. 338–342.

    Article  Google Scholar 

  41. Kerani RP, Handcock MS, Handsfield HH, Holmes KK (2005) Comparative geographic concentrations of 4 sexually transmitted infections. American Journal of Public Health 95(2):324–330.

    Article  Google Scholar 

  42. Green CG, Krause D, Wylie J. (2006) Spatial analysis of Campylobacter infection in the Canadian province of Manitoba. International Journal of Health Geographics 5(1):2.

    Article  Google Scholar 

  43. Fine PEM, Clarkson JA (1982) Measles in England and Wales- 1: An analysis of factors underlying seasonal patterns. International Journal of Epidemiology. 11(1):5–14.

    Article  Google Scholar 

  44. Grassly NC, Fraser C (2006) Seasonal infectious disease epidemiology. Proceedings of the Royal Society B: Biological Sciences. 273:2541–2550.

    Article  Google Scholar 

  45. Chowell G, Bettencourt LM, Johnson N, Alonso WJ, Viboud C (2008) The 1918–1919 influenza pandemic in England and Wales: Spatial patterns in transmissibility and mortality impact. Proceedings of the Royal Society B: Biological Sciences. 275:501–509.

    Article  Google Scholar 

  46. Diekmann O, Jong MCMD, Koeijer AAD, Reijnders P (1995) The force of infection in populations of varying size: A modelling problem. Journal of Biological Systems. 3(2):519–529.

    Article  Google Scholar 

  47. Jong MCMD, Diekmann O, Heesterbeck H (1995) Epidemic Models: Their Structure and Relation to Data. How does transmission of infection depend on population size. Cambridge University Press

    Google Scholar 

  48. McCallum H, Barlow N, Hone J (2001) How should pathogen transmission be modelled? TRENDS in Ecology & Evolution 16(6):295–300.

    Article  Google Scholar 

  49. Chowell G, Torre CA, Munayco-Escate C, Suarez-Ognio L, Lopez Cruz RL, Hyman JM, et al. (2008) Spatial and temporal dynamics of dengue fever in Peru: 1994–2006. Epidemiology and Infection 136(12):1667–77.

    Article  Google Scholar 

  50. Panagiotopoulos T, Antoniadou I, Valassi-Adam E (1999) Increase in congential rubella occurence after immunisation in Greece: Retrospective survey and systematic review. BMJ. 319:1462–1467.

    Google Scholar 

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Author information

Authors and Affiliations

  1. School of Human Evolution and Social Change, Arizona State University, Tempe, AZ 85287, USA

    Daniel Rios-Doria

  2. Mathematical, Computational, Modeling Sciences Center, Arizona State University, Tempe, AZ 85287, USA

    Daniel Rios-Doria

  3. School of Human Evolution and Social Change, Arizona State University, Box 872402, Tempe, AZ 85287, USA

    Gerardo Chowell

  4. Mathematical, Computational, Modeling Sciences Center, Arizona State University, Tempe, AZ 85287, USA

    Gerardo Chowell

  5. Division of Epidemiology and Population Studies, Fogarty International Center, National Institutes of Health, Bethesda, MD, USA

    Gerardo Chowell

  6. Dirección General de Epidemiología, Ministerio de Salud, Perú, Jr. Camilo-Carrillo 402, Jesus Maria-Lima 11, Peru

    Cesar Munayco-Escate

  7. Dirección General de Epidemiología, Ministerio de Salud, Perú, Jr. Camilo-Carrillo 402, Jesus Maria-Lima 11, Perú

    Alvaro Witthembury

  8. Mathematical, Computational, and Modeling Sciences Center, P.O. Box 871904, Arizona State University, Tempe, AZ 85287, USA

    Carlos Castillo-Chavez

  9. School of Human Evolution and Social Change, Arizona State University, Tempe, AZ 85287, USA

    Carlos Castillo-Chavez

  10. Department of Mathematics and Statistics, Arizona State University, Tempe, AZ, 85287, USA

    Carlos Castillo-Chavez

  11. Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, NM 87501, USA

    Carlos Castillo-Chavez

Authors
  1. Daniel Rios-Doria
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  2. Gerardo Chowell
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  3. Cesar Munayco-Escate
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  4. Alvaro Witthembury
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  5. Carlos Castillo-Chavez
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Editor information

Editors and Affiliations

  1. Arizona State University School of Human Evolution & Social Change, Tempe, AZ 85287-2402, USA

    Gerardo Chowell

  2. Los Alamos National Laboratory, Mail Stop B284, Los Alamos, NM 87545, USA

    James M. Hyman  & Luís M. A. Bettencourt  & 

  3. Dept. Mathematics & Statistics, Arizona State University, P.O.Box 871804, Tempe, AZ 85287, USA

    Carlos Castillo-Chavez

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Rios-Doria, D., Chowell, G., Munayco-Escate, C., Witthembury, A., Castillo-Chavez, C. (2009). Spatial and Temporal Dynamics of Rubella in Peru, 1997–2006: Geographic Patterns, Age at Infection and Estimation of Transmissibility. In: Chowell, G., Hyman, J.M., Bettencourt, L.M.A., Castillo-Chavez, C. (eds) Mathematical and Statistical Estimation Approaches in Epidemiology. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-2313-1_13

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