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Time Series Analysis

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Epidemics

Part of the book series: Use R! ((USE R))

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Abstract

Analysis of epidemic time series is a large endeavor because of the richness of dynamical patterns and a plentitude of historical data (Rohani & King, 2010). A wide range of tools are used, some of which are borrowed from mainstream statistics and other of which are custom-made. The classic “mainstream” methods belong to two categories: the so-called time-domain and frequency-domain methods. The autocorrelation function and ARIMA models belong to the former class and spectral analysis , and the periodogram belongs to the latter. Hybrid time/frequency methods have become increasingly prominent in the form of wavelet analysis because it allows the study of changes in disease dynamics through time (Grenfell et al., 2001).

This chapter uses the following R packages: forecast, Rwave, imputeTS, nlts , and plotrix.

Five minute epidemic MOOC videos on seasonality and patterns of endemicity can be watched on YouTube:

Seasonality https://www.youtube.com/watch?v=TDuuM-wm6nw

Patterns of endemicity https://www.youtube.com/watch?v=Mf_EZm5amxI .

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Notes

  1. 1.

    The ARMA model is usually considered a purely statistical model (i.e., not containing biological mechanism), though it can be shown that for example the linearized discrete-time SIR model with stochastic transmission can be approximately mapped onto an ARMA(2,1) model (see Sect. 10.9). Bjørnstad et al. (2001) and Bjørnstad et al. (2004) provide additional examples of how ARMA processes arise from a variety of ecological interactions.

  2. 2.

    The first smallpox vaccines are dated to China in the fifteenth century (Plotkin, 2011). Thereafter, the diphteria toxoid vaccine developed in the 1920s was among the very first to be broadly administered (Relyveld, 2011).

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Authors and Affiliations

  1. Center for Infectious Disease Dynamics, Pennsylvania State University, University Park, PA, USA

    Ottar Bjørnstad

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  1. Ottar Bjørnstad
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Bjørnstad, O. (2023). Time Series Analysis. In: Epidemics. Use R!. Springer, Cham. https://doi.org/10.1007/978-3-031-12056-5_7

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