Some countries including Kazakhstan conduct surveillance for hospitalised cases presenting with a severe acute respiratory infection (SARI). The prediction of new SARI cases is one of the steps taken by the competent structures of the health system in the development of measures to control and manage the non-proliferation of various viral diseases. Considering that the COVID-19 pandemic had a direct impact on the number of SARI, in this research, based on time series analysis, an attempt was made to build and compare different SARI time series forecasting models. Baseline data for SARI cases in Kazakhstan was taken from the European Center for Disease Prevention and Control (ECDC). Forecasts for one and two years were obtained from time series forecasting models ARIMA and TBATS. Models were built on the three training sets, all starting from October 2015, and in the first case ended far from the COVID-19 pandemic period, in the second case ended in the pre-pandemic period, in the third case – included one year of pandemic. The 1st period was from October 2015 to October 2018, and forecasts were for the next one (2019) and two (2019-2020) years. The following models were obtained: ARIMA(1,0,0)(0,1,0)[12] with coefficients: ar1=0.878; s.e. =0.078 and accuracy according to MAPE=28.27 and MAPE=48.35 for 2019 year and (2019-2020) years of prediction respectively. TBATS(1, {0,0},-, {<12,5>}) with next parameters: Alpha =1.076; Gamma-1 Values=0.009; Gamma-2 Values =0.010 and MAPE=37.56 and MAPE=44.17 for 2019 year and (2019-2020) years of prediction respectively. The 2nd period was from October 2015 to February 2020, with forecasts were for the next one (2021) and two (2021-2022) years. The models were obtained: ARIMA(1,0,0)(0,1,0)[12] with coefficients: ar1=0.849; s.e.=0.076 and accuracy according to MAPE=165.0 and MAPE=101.9 for 2021 year and (2021-2022) years of prediction respectively. TBATS(1, {0,0},-, {<12,5>}) with next parameters: Alpha =0.839; Gamma-1 Values=-0.005; Gamma-2 Values =0.012 and MAPE=86.11 and MAPE=60.12 for 2021 year and (2021-2022) years of prediction respectively. The 3rd period was from October 2015 to March 2021 and a forecast was for the next 13 months. The models were obtained: ARIMA(0,1,0)(1,1,0)[12] with coefficients: sar1=-0.278; s.e.=0.170 and accuracy for 13 months prediction: MAPE=53.73. TBATS(1, {0,0},-, {<12,5>}) with next parameters: Alpha =0.995; Gamma-1 Values=-0.011; Gamma-2 Values =0.009 and accuracy for 13 months prediction: MAPE=44.39. The following regularities were identified in this research: the TBATS time series forecasting models compared to ARIMA models showed greater accuracy in the most cases of forecasts. SARI prediction accuracy for both created models was worst when the pre-COVID period was taken as the training set, and the forecast was already made for the period with the current COVID-19 pandemic. This research has been funded by the Ministry of Health of the Republic of Kazakhstan (Program No. BR11065386) [ABSTRACT FROM AUTHOR]