COVID-19 has become the most important and crucial agenda in the world in the last year. COVID-19 has taken many lives around the world and millions of people have been infected. To get rid of this depression caused by COVID-19, many countries have started big campaigns for vaccine production. In this study, data on infection cases and vaccinations conducted in England, Germany, Israel, Russia, and the USA were analyzed from January 3, 2020, to March 3, 2021. We used univariate time series models, where the results are very accurate, rather than epmdicolgical models. In this article we used BATS, TBATS, Holt’s linear trend, and ARIMA models to recognize the pattern of spread of covid 19 infection cases. The best models are specified for all countries that have the least error according to MAPE. Findings obtained in this study have been reported extensively in England, Germany, Israel, Russia, and the USA with tables and figures. Using the results and forecasts obtained in this study, England, Germany, Israel, Russia, and the USA can take COVID-19 measures for the future.