This paper aims to study how the increase in vaccination rate in Israel affect to the behavior of COVID-19 reproduction rate, from 19 December 2020, to 25 April 2021. Multiple advanced econometrics methodologies are used to analyze the degree of persistence, to understand the relationship between these two times series and the long-term behavior. The results of our study indicate that the vaccinations cause long-run effects to COVID-19 reproduction rate and the vaccination provides useful information to predict the COVID-19 reproduction rate. Also, we determine whatever exogenous shocks related with the virus reproduction will have a very short impact over time. The first change in trend occurs on 13 January 2021, with 24.37% of the population vaccinated and when it can be seen that the increased rate of vaccinations causes the infection rate to decrease.