Stochastic modelling of scalar time series of varicella incidence for a period of 92 years (1928-2019).

Abstract

Varicella is an acute, highly contagious disease, characterised by generalised vesicular exanthema caused by the initial infection with varicella zoster virus (VZV) which usually affects children aged 2 to 8 years. To analyse the changes of varicella incidence in Bulgaria over the period of 1928-2019. The time series analysis is based on the official data for varicella incidence (per 100,000) in Bulgaria for ninety-two years (1928-2019), obtained from three major sources. We utilized the method to construct a time series model of overall incidence (1928-2019) using time series modeller in SPSS v. 25. We followed all three steps of the standard ARIMA methodology to establish the model - identification, parameter estimation, and diagnostic checking. Stochastic scalar time series modelling of the varicella incidence from 1928 to 2019 was performed. The stochastic ARIMA (0,1,1) was identified to be the most appropriate model. The decomposition of varicella incidence time series into a stochastic trend and a stationary component was reasoned based on the model defined. In addition, we assessed the importance of the long-term and immediate effect of one shock. The long-term forecast was also under discussion. The ARIMA model (0,1,1) in our study is an adequate tool for presenting the varicella incidence trend and is suitable to forecast near future disease dynamics with acceptable error tolerance.