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This study examines the success of COVID-19 vaccines in four European countries and Israel for the α variant. These countries respond to the vaccines with varying degrees of success. Countries with successful vaccination programs take about 160 days to get to the minimum number of new cases. Only Italy and Israel came close to eradicating the virus. Vaccines and previous infections have a similar prophylactic effect on new infections. Second doses for the most part add little protection to those who have only one dose. Vaccines become very effective after seven days although there are some added benefits that accrue to individuals in the second week after vaccination. The effect of vaccines on new cases is non-linear and exhibits a decreasing marginal effect. COVID-19 is spread by asymptomatic carriers, a feature of the disease which was discernable at the same time that public health agencies were discouraging the use of masks by the general public and downplaying the importance of social distancing. These were major policy errors and led to many unnecessary deaths.

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