Stochastic modeling of empirical time series of childhood infectious diseases data before and after mass vaccination
Open Access
- 8 August 2006
- journal article
- Published by Springer Science and Business Media LLC in Emerging Themes in Epidemiology
- Vol. 3 (1), 9
- https://doi.org/10.1186/1742-7622-3-9
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.Keywords
This publication has 42 references indexed in Scilit:
- Comparison of Vaccination with Measles-Mumps-Rubella Vaccine at 9, 12, and 15 Months of AgeThe Journal of Infectious Diseases, 2004
- Do variations in pertussis notifications reflect incidence or surveillance practices? A comparison of infant notification rates and hospitalisation data in NSWNew South Wales Public Health Bulletin, 2003
- Failure of Physicians to Consider the Diagnosis of Pertussis in ChildrenClinical Infectious Diseases, 1999
- Estimates of the effectiveness of a whole-cell pertussis vaccine from an outbreak in an immunized populationVaccine, 1997
- Spatial heterogeneity, nonlinear dynamics and chaos in infectious diseasesStatistical Methods in Medical Research, 1995
- The Croonian Lecture, 1994. Populations, infectious disease and immunity: a very nonlinear worldPhilosophical Transactions Of The Royal Society B-Biological Sciences, 1994
- Chaos and biological complexity in measles dynamicsProceedings Of The Royal Society B-Biological Sciences, 1993
- Chaos and complexity in measles models: A comparative numerical studyMathematical Medicine and Biology, 1993
- Estimating the Dimension of a ModelThe Annals of Statistics, 1978
- The Critical Community Size for Measles in the United StatesJournal of the Royal Statistical Society. Series A (General), 1960