Effect of vaccination against COVID-19 spreading

We continue (Ref. 1: Proc. Jpn. Acad. Ser. B 97, 22-49) to analyze the COVID-19 status. We concentrate on the following issues in this work: 1. Effect of vaccination against the spreading of SARS-CoV-2. 2. General landscape of the world situation concerning vaccinations. 3. Some aspects of the new variants of SARS-CoV-2. Our findings include: 1. With vaccinations, it is fair to say that we have entered a new phase in the fight against the virus SARS-CoV-2. We have analyzed some preliminary data to find how vaccinations can be effective against COVID-19 spreading. This analysis is based on, and is a continuation of, our first paper quoted in Ref. 1. 2. If Tokyo (or Japan) continues to keep its vaccination schedule (starting in early April, 2021 and finishing it for elderly, 65 or older, in 4 months), it will see a sign of control of the virus in early June, 2021 although we see changes of this status due to new, more contagious variants. 3. The strength (parameter beta) of a new contagious variant can be estimated based on the initial data on the variant (Section 5).