Methodology

Stochastic modeling of empirical time series of childhood infectious diseases data before and after mass vaccination

Helen Trottier^1,3 , Pierre Philippe¹ and Roch Roy²

¹  Department of Social & Preventive Medecine, University of Montréal, Montréal, Canada

²  Department of Mathematics and Statistics, University of Montréal, Montréal, Canada

³  Department of Oncology, Division of Cancer Epidemiology, McGill University, 546 Pine Avenue West, Montréal, Qc., Canada

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Emerging Themes in Epidemiology 2006, 3:9doi:10.1186/1742-7622-3-9

Published:	8 August 2006

Abstract

The goal of this paper is to analyze the stochastic dynamics of childhood infectious disease time series. We present an univariate time series analysis of pertussis, mumps, measles and rubella based on Box-Jenkins or AutoRegressive Integrated Moving Average (ARIMA) modeling. The method, which enables the dependency structure embedded in time series data to be modeled, has potential research applications in studies of infectious disease dynamics. Canadian chronological series of pertussis, mumps, measles and rubella, before and after mass vaccination, are analyzed to characterize the statistical structure of these diseases. Despite the fact that these infectious diseases are biologically different, it is found that they are all represented by simple models with the same basic statistical structure. Aside from seasonal effects, the number of new cases is given by the incidence in the previous period and by periodically recurrent random factors. It is also shown that mass vaccination does not change this stochastic dependency. We conclude that the Box-Jenkins methodology does identify the collective pattern of the dynamics, but not the specifics of the diseases at the biological individual level.