  By the end of 2020, a year since the first cases of infection by the Covid-19
virus have been reported, there is a light at the end of the tunnel. Several
pharmaceutical companies made significant progress in developing effective
vaccines against the Covid-19 virus that has claimed the lives of more than a
million people over the world. On the other hand, there is growing evidence of
re-infection by the virus, which can cause further outbreaks. In this paper, we
apply statistical physics tools to examine the vaccination rate required to
control the pandemic for three different vaccine efficiency scenarios. Also, we
study the effect of temporal restrictions/reliefs on the pandemic's outbreak,
assuming that re-infection is possible. When examining the efficiency of the
vaccination rate of the general population in preventing an additional outbreak
of the disease, we find that a high vaccination rate (where at least 0.3% of
the population is vaccinated daily, which is equivalent to ~ 1 million vaccine
doses in the United States daily) is required to gain control over the spread
of the virus without further restrictions. Due to feasible limitations on the
vaccination rate, the vaccination process should be accompanied by the
prevailing restrictions until most of the population is vaccinated.
