I was curious about the man for whom this medical group is named, so I looked it up:
(edited to add text, as the wikilink goes to a different Henry Reeve!)
http://en.wikipedia.org/wiki/Henry_Reeve_(soldier)
Henry Reeve (1850—1876) was a Brigadier General in Cuba's 'Ejército Libertador' - more commonly known as the 'Ejército Mambi' - during the Ten Years' War (1868-1878).
He was born in Brooklyn, New York, USA on April 4, 1850 and died in Matanzas, Cuba on August 4, 1876. Reeve was 27 years old at the time of his death, and had served in the Cuban Army for 7 years having participated in over 400 battles against the Spanish Army.
Upon becoming aware of the Cuban uprising initiated at 'La Demajagua' by Carlos Manuel de Cespedes in 1868, he promptly volunteered. He arrived in Cuba in 1869 aboard the ship Perrit as part of an Expeditionary Force.
The expedition was ambushed by the Spanish Army while unloading and Reeve was taken prisoner along with many others. A Spanish firing squad shot the group, and left them unburied and presumed dead. Reeve was wounded but had enough strength to creep away, and was found by units of the Cuban Army.
He was known as 'Enrique - El Americano' and nicknamed "El Inglesito" by Ignacio Agramonte y Loynáz, and he quickly rose under his command. Reeve in turn gave Agramonte his nickname: "El Mayor". He served with distinction initially under Agramonte and subsequently under Máximo Gómez y Báez.
Under Agramonte he participated in many actions, including the rescue of Julio Sanguily in 1871 where Agramonte, Reeve, and 34 others overcame a superior Spanish force of 120.
In one critical action he jumped over an artillery battery, lifting the morale of the Cuban fighters but was seriously wounded on a leg. For his actions he was promoted to the rank of Brigadier General.
Exposed to the harsh jungle conditions, he was told he would never walk or ride a horse again. Reeve persevered and with metallic braces he was able to walk, but had to be strapped to his mount in order to be able to ride his horse. He kept leading the famed Camagüey Cavalry Corps throughout the balance of his life.
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In response to Hurricane Katrina, Cuba assembled 1,586 humanitarian doctors to offer to assist the United States. The offer was declined, and on September 19, 2005 Fidel Castro created the Henry Reeves International Contingent of Doctors Specialized in Disasters and Serious Epidemics in honor of him.