Several researchers have used standard time series models to analyze future patterns of COVID-19 and the Causal impact of vaccinations in various countries. Bayesian structural time series (BSTS) and ARIMA (Autoregressive Integrated Moving Average) models are used to forecast time series. The goal of this study is to look at a much more adaptable effective methodology for dissecting the major components of a time series that breaks down the main parts of a time series. Within the period of March 1, 2020, to June 30, 2021, we used these state space model to explore the forecast patterns of COVID-19 in five afflicted nations.In addition, we used intervention analysis under BSTS models to examine the casual effect of vaccines in these countries, and we reached higher levels of accuracy than ARIMA models. According to forecasts, the number of confirmed cases in the United States, the United Kingdom, the United Arab Emirates, Bahrain, and India will climb by 1.17%, 19.4%, 15.5%, 13.8% , and 8%, respectively, during the next 60 days. On the other side, death rates in the United States, the United Kingdom, the United Arab Emirates, Bahrain, and India are expected to rise by 2.7%, 3.5%, 15.8%, 9.4%, and 14.8%, respectively. In addition, By using effective and quick vaccination, the United States, United Kingdom, and UAE have been able to reduce the number of mortality. On the other hand, vaccination is currently unable to decrease the rate of cases and deaths in India. Overall, the Indian healthcare system is likely to be seriously over-burdened in the next month. Though the USA and UK have managed to cut down the rates of COVID-19 deaths,but in UK and UAE number of confirmed cases are high as compared to other nations,so serious efforts will be required to keep these controllable. On the other hand,To keep things under control, Bahrain and four other countries has to speed up vaccinations.