HAVANA, Dec 29 (Reuters) - Cuba will give booster shots to its entire population in January, according to a report in state-run media, in a bid to keep the highly contagious Omicron variant of the coronavirus at bay. Health authorities in the island, heavily dependent on tourism, last week reported a 35% week-on-week jump in coronavirus cases. As of Tuesday, they had registered at least 44 cases of Omicron, though both infections and deaths from COVID-19 remain at 1% of their pandemic peak on Aug. 22, according to statistics compiled by the online database "Our World in Data". Health Minister Jose Angel Portal Miranda said the threat from Omicron had prompted Cuba to fast-track its booster campaign, and that all those eligible would have a booster shot in January, according to the state news outlet CubaDebate. Cuba has already administered nearly 1.5 million boosters in the capital Havana, and to high risk groups such as health care workers. That campaign will now spread across the island in the coming weeks. The poor, communist-run nation has vaccinated 92% of its population with at least one shot, and 85% with a full course, of its homegrown vaccines, according to "Our World in Data." That puts it second in the world behind only the United Arab Emirates, among countries of at least 1 million people. read more Cuba has vaulted ahead of its neighbors in Latin America and other emerging economies by developing its own vaccines instead of competing for those produced by wealthier nations. Officials say Cuba"s protein-based shots - Abdala, Soberana 02 and Soberana Plus - give upwards of 90% protection against symptomatic COVID-19 when offered in three-dose schemes, though those claims have yet to be fully vetted in peer-reviewed journals, or by the World Health Organization. Cuban scientists had previously called for boosters to be given six months after the first three shots, but have now halved that time, the CubaDebate report said.