HOUSTON, Jan 10 (Reuters) - Texas will allocate about half of its latest COVID-19 vaccine supplies to just 28 healthcare sites, officials said on Sunday, aiming to speed distribution amid rising infections and hospitalizations.

Distribution efforts in the second most-populous U.S. state have been falling short, with people forced to wait for hours, online registration sites unable to keep up, or vaccine locations abruptly changed because of overwhelming demand.

The state's positivity rate, or percent of cases testing positive, was 19.2% on Saturday, up nearly 6 percentage points in the past four weeks. New infections rose by nearly 19,000 and more than 13,000 people were hospitalized, up 4,000 in the past four weeks.

Concentrating deliveries will simplify sign ups and provide more shots to eligible residents, the state said in a news release. First-shot allocations are based on estimates of how many people each location could serve. Department of State Health Services officials were not available to comment.

Of the 310,000 doses expected this week in Texas, about 159,000 will be delivered to just 28 locations. Smaller sites will split 38,300 doses and nursing home and long-term care facilities will get 121,875, the state said.

(Reporting by Gary McWilliams; Editing by Peter Cooney)