A study recently published in the Washington Post indicated that the dramatically lower rate of total infections and deaths in the USA masks the fact that in the USA, the pandemic is still raging at the same level as in January within the unvaccinated community. The study strongly suggests that the pandemic would be pretty much completely done in the USA if we had a higher vaccination rate.
I just checked several websites related to the Caymans. The data are not the same in each, but they have had about 580 cases and 2 deaths total, so the shutdown has been effective. Roughly 60% of the island is fully vaccinated, and at the current rate, it should be over 70% within a month. That is well beyond the USA's numbers, and close to what some experts have said would be herd immunity.
According to articles I read, vaccine hesitancy is a problem throughout the Caribbean, and it is the primary hindrance to a return of the tourism industry. The only article I found specific to the Caymans was more than a month old, but it indicated there had been a sharp decline in the vaccination rates, indicating a fairly large percentage of the population is resisting vaccination.