Data Analysis and Related Applications, Volume 1

22Using Parameters of Piecewise Approximation by Exponents for Epidemiological Time Series Data Analysis

Nowadays, detailed epidemiological data are available in the form of time series data (or as an array): N[k] – where N is the documented number of events registered at the equidistant time moments T(k) = To + k*delta (e.g. “Number of newly reported cases of Covid-19 in the last 24 hours” – published on a daily basis by WHO). Theoretically, those data can be adequately described by different dynamic models containing exponential growth and exponential decay elements. Practically, parameters of those models are not constants – they can change in time because of many factors like changing hygiene policies, changing social behavior and vaccination. Hence, it was decided to use a piecewise approach: short sequential fragments of time series data are approximated by a function containing some parameters. The above parameters are evaluated for the first time series data fragment. Then, the next data fragments are processed. As a result, new time series data (arrays) are created: evaluated sequences of parameters. Those new series can be considered and analyzed as functions of time. In the simplest example, the function to be used for every fragment is A + B*exp( alpha* t). The resulting values of A, B and alpha in that case are time series data – arrays: A[k], B[k] and alpha[k] known at the equidistant time moments T(k). By plotting those sequences, it can be seen if the simple ...