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Pollard had been ruled out of West Indies' tour of Pakistan in December because of a hamstring injury, with Nicholas Pooran leading the T20I side in his absence. Shai Hope had been due to take charge in the ODIs, before they were called off due to rising Covid-19 infections among the party.
Former captain Jason Holder is also back in both squads, but there was no room for Andre Russell, despite his recent spell in the Big Bash League. Obed McCoy was not included due to a shin injury suffered at the T20 World Cup.
There had been suggestions that the Ireland T20I at Sabina Park could provide the stage for Chris Gayle's farewell from international cricket, but he has not been named in the squad, amid reports a testimonial match could be arranged for later in the year.
Allrounder Allen, who missed the World Cup with an ankle injury, has been passed fit despite testing positive for Covid and is expected to be available for the England series later in the month.
"We have tried to maintain the general make-up of the squads from the Pakistan tour before Christmas, with the captain and some senior players coming back in," West Indies head coach, Phil Simmons, said. "Covid-19 has also played a part in the final make-up of the squad. The challenges in the next couple months are getting the young players in both squads to not only improve on their skills but maintain the attitude and desire we saw in Pakistan.
"We do need to start the year on a high. And we know both Ireland and England have very good teams, so we expect a very strong challenge as we look improve our chances of automatic qualification for the ICC Cricket World Cup in 2023 and building the T20 team for the ICC T20 World Cup in 2022."
West Indies will play Ireland in three ODIs in Jamaica, starting on January 8, followed by a one-off T20I. They will then host England in Barbados for a five-match T20I series.
Ireland's tour of the USA and Caribbean has also been hit by Covid-19. The ODI leg against USA was cancelled due to a number of positive tests, with Paul Stirling and Shane Getkate set to miss the first West Indies fixture while isolating in their hotel in Florida.
West Indies ODI squad: Kieron Pollard (capt), Shai Hope, Shamarh Brooks, Roston Chase, Justin Greaves, Jason Holder, Akeal Hosein, Alzarri Joseph, Gudakesh Motie, Jayden Seales, Nicholas Pooran, Romario Shepherd, Odean Smith, Devon Thomas
Reserves: Keacy Carty, Sheldon Cottrell
West Indies T20I squad: Kieron Pollard (capt), Nicholas Pooran, Fabian Allen (England T20Is only), Darren Bravo (England T20Is only), Roston Chase, Sheldon Cottrell, Dominic Drakes, Shai Hope, Akeal Hosein, Jason Holder, Brandon King, Kyle Mayers, Rovman Powell, Romario Shepherd, Odean Smith, Hayden Walsh Jr
Reserves: Jayden Seales, Alzarri Joseph, Devon Thomas