This paper uses time series econometric techniques to analyze American Covid 19 data from February 2020 to the end of October 2022. Distributed lag models are employed to uncover the unobservable effects that occur when uninfected individuals come in contact with other individuals whose Covid status is unknown. The purpose of the study is to compare the immunological benefits of vaccinations with those that arise from a previous infection. The main results obtained here is that this relation depends on the variant being considered: earlier variants produced similar benefits whereas the benefits from being previously infected by the Delta and Omicron varieties provided considerably less protection against further infection. The benefits from infection by other variants were also shown to be small for the variant under consideration casting doubt on the idea that herd immunity might be possible.