Gov. Andrew M. Cuomo of New York said that hospitals could face fines of up to $100,000 if they did not use their current supplies of vaccine by the end of the week. Britain imposed a strict new national lockdown.

The number of inmates and guards known to have been infected with the coronavirus at American correctional institutions exceeded 500,000 on Monday, according to a New York Times database.

As correctional institutions have been battered by coronavirus infections and deaths, the number of cases reported in has risen by nearly 84 percent in the last two months, according to a Times analysis of the data from some 2,600 prisons, jails and immigration detention centers.

There are now 88 facilities that have had at least 1,000 infections, according to the database.

Local jails and state prison systems have been so devastated by the virus that they have resorted to the drastic strategy of shutting down completely and transferring inmates elsewhere. Experts say the jails and prisons that stay open will probably become even more crowded, unsanitary and disease ridden, and the transfers are likely to help the virus proliferate both inside and outside the walls.

At the same time, some states, like 

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