Chapter

Mathematical and Statistical Estimation Approaches in Epidemiology

pp 325-341

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

  • Daniel Rios-DoriaAffiliated withSchool of Human Evolution and Social Change, Arizona State UniversityMathematical, Computational, Modeling Sciences Center, Arizona State University
  • , Gerardo ChowellAffiliated withSchool of Human Evolution and Social Change, Arizona State UniversityMathematical, Computational, Modeling Sciences Center, Arizona State UniversityDivision of Epidemiology and Population Studies, Fogarty International Center, National Institutes of Health
  • , Cesar Munayco-EscateAffiliated withDirección General de Epidemiología, Ministerio de Salud, Perú, Jr. Camilo-Carrillo 402
  • , Alvaro WitthemburyAffiliated withDirección General de Epidemiología, Ministerio de Salud, Perú, Jr. Camilo-Carrillo 402
  • , Carlos Castillo-ChavezAffiliated withMathematical, Computational, and Modeling Sciences Center, P.O. Box 871904, Arizona State UniversitySchool of Human Evolution and Social Change, Arizona State UniversityDepartment of Mathematics and Statistics, Arizona State UniversitySanta Fe Institute

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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.

Keywords

Rubella Peru Epidemic Periodicity Reproduction number Age at infection