Statistical mechanics study of the introduction of a vaccine against COVID-19 disease

By the end of 2020, a year since the first cases of infection by the Covid-19 virus have been reported; several pharmaceutical companies made significant progress in developing effective vaccines against the Covid-19 virus that has claimed the lives of more than 10^{6} 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 theoretically the vaccination rate required to control the pandemic for three different vaccine efficiency scenarios and five different vaccination rates. Also, we study the effect of temporal restrictions or 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 0.3% of the population is vaccinated daily, which is equivalent to ≈10^{6} vaccine doses in the United States daily) is required to gain control over the spread of the virus without further restrictions.