  Besides maintaining health precautions, vaccination has been the only
prevention from SARS-CoV-2, though no clinically proved 100% effective vaccine
has been developed till date. At this stage, to withhold the debris of this
pandemic, experts need to know the impact of the vaccine efficacy rate's
threshold and how long this pandemic may extent with vaccines that have
different efficacy rates. In this article, a mathematical model study has been
done on the importance of vaccination and vaccine efficiency rate during an
ongoing pandemic. We simulated a five compartment mathematical model to analyze
the pandemic scenario in both California, and whole U.S. We considered four
vaccines, Pfizer, Moderna, AstraZeneca, and Johnson and Johnson, which are
being used rigorously to control the COVID-19 pandemic, in addition with two
special cases: a vaccine with 100% efficacy rate and no vaccine under use. Both
the infection and death rates are very high in California. Our model suggests
that the pandemic situation in California will be under control in the last
quartile of the year 2023 if frequent vaccination is continued with the Pfizer
vaccine. During this time, six waves will happen from the beginning of the
immunization where the case fatality and recovery rates will be 1.697% and
98.30%, respectively. However, according to the considered model, this period
might be extended to the mid of 2024 when vaccines with lower efficacy rates
are used. The more effective a vaccine, the less people suffer from this malign
infection. Although specific groups of people get prioritized initially, mass
vaccination is needed to control the spread of the disease.
