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

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.