1. Many demographic and ecological processes generate seasonal and other periodicities. Seasonality in infectious disease transmission can result from climatic forces such as temperature and humidity; variation in contact rates as a result of migration or school calendar; or temporary surges in birth rates. Seasonal drivers of acute immunizing infections can also drive longer‐term fluctuations.
2. Tensor decomposition has been used in many disciplines to uncover dominant trends in multi‐dimensional data. We introduce tensors as a novel method for decomposing oscillatory infectious disease time series.
3. We illustrate the reliability of the method by applying it to simulated data. We then present decompositions of measles data from England and Wales. This paper leverages simulations as well as much‐studied data to illustrate the power of tensor decomposition to uncover dominant epidemic signals as well as variation in space and time. We then use tensor decomposition to uncover new findings and demonstrate the potential power of the method for disease incidence data. In particular, we are able to distinguish between annual and biennial signals across locations and shifts in these signals over time.
4. Tensor decomposition is able to isolate variation in disease seasonality as a result of variation in demographic rates. The method allows us to discern variation in the strength of such signals by space and population size. Tensors provide an opportunity for a concise approach to uncovering heterogeneity in disease transmission across space and time in large datasets.

中文翻译：

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传染病发病数据的张量分解

1. 
   许多人口和生态过程产生季节性和其他周期性。传染病传播的季节性可能是由温度和湿度等气候因素造成的；由于移民或学校日历而导致联系率发生变化；或出生率暂时激增。急性免疫感染的季节性驱动因素也可能导致长期波动。
2. 
   张量分解已在许多学科中用于揭示多维数据的主导趋势。我们引入张量作为分解振荡传染病时间序列的新方法。
3. 
   我们通过将其应用于模拟数据来说明该方法的可靠性。然后，我们对英格兰和威尔士的麻疹数据进行分解。本文利用模拟以及经过大量研究的数据来说明张量分解在揭示主要流行病信号以及空间和时间变化方面的力量。然后，我们使用张量分解来发现新的发现，并证明该方法在疾病发病率数据方面的潜在能力。特别是，我们能够区分不同地点的年度和两年期信号以及这些信号随时间的变化。
4. 
   张量分解能够分离由于人口比率变化而导致的疾病季节性变化。该方法使我们能够根据空间和人口规模辨别此类信号强度的变化。张量提供了一种简洁的方法来揭示大型数据集中跨空间和时间的疾病传播的异质性。