HONG KONG — Countries, cities and businesses across the globe issued new travel warnings on Tuesday, vastly expanding a cordon intended to control the flow of people to and from China, where the authorities are struggling to contain the outbreak of the new coronavirus.

In the most drastic measure to limit travel, the Hong Kong authorities reduced by half the number of flights and shut down rail service to mainland China, and they also limited visas — moves that could inspire other governments to follow suit.

Measures to contain the outbreak of the virus to its epicenter in Hubei Province appear to have failed to stop the contagion.

On Wednesday morning, Chinese officials said the number of cases had increased by nearly a third overnight. Experts warned that the actual number of cases could be significantly higher and growing quickly. The number of deaths attributed to the virus also continued to grow.