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

机译：大规模疫苗接种前后儿童传染病经验时间序列的随机建模

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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.
机译：本文的目的是分析儿童传染病时间序列的随机动态。我们基于Box-Jenkins或自回归综合移动平均线（ARIMA）建模提出了百日咳，腮腺炎，麻疹和风疹的单变量时间序列分析。该方法可以对嵌入在时间序列数据中的依存关系结构进行建模，在传染病动力学研究中具有潜在的研究应用。对加拿大百日咳，腮腺炎，麻疹和风疹的按时间顺序排列的疫苗进行了分析，以分析这些疾病的统计结构。尽管这些传染病在生物学上是不同的，但发现它们全部由具有相同基本统计结构的简单模型表示。除了季节性影响之外，新病例的数量还取决于前一时期的发病率和定期复发的随机因素。还表明，大规模疫苗接种不会改变这种随机依赖性。我们得出的结论是，Box-Jenkins方法论确实确定了动力学的集体模式，但并未确定生物个体水平上疾病的具体特征。

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