The thaw in relations between the US and Cuba has led to a stunning 36% increase in visits by Americans to the island, including thousands who are flying into Cuba from third countries like Mexico in order to sidestep US restrictions on tourism.

The dramatic rise was seen in the number of Americans with no family ties to Cuba who visited between 1 January and 9 May of this year compared to the same period in 2014, according to statistics provided to the Associated Press by a University of Havana professor.

In addition to the boom in American visitors, Cuba has seen a 14% jump in arrivals from around the world between January and early May compared to the same period last year.

From 1 January to 9 May, 51,458 Americans visited Cuba, compared to 37,459 over that period last year, according to new statistics provided exclusively to the Associated Press by Jose Luis Perello Cabrera, an economist in the University of Havana’s tourism studies department with access to official figures. The figures also included revealing details on the thousands of Americans who are entering Cuba through third countries, many to sidestep US restrictions on tourism.

There were 38,476 visitors who flew directly from the US to Cuba, compared to 29,213 in the same period last year.

Another 12,982 Americans came in via third countries, a whopping 57% increase over the 8,246 Americans who flew to Cuba from elsewhere in the same period last year.

Mexico, the Bahamas, Jamaica and the Cayman Islands are the top choices for Americans entering Cuba from non-US points, Perello said.

David Perez, a New Yorker who works in public relations, traveled to Cuba in May through Cancun. “I had just always wanted to go to Cuba and I decided now was the time,” he said.

Cuba also has seen a 14% rise in overall tourism. Arrivals from 206 counties from 1 January to 9 May rose from 1,349,903 last year to 1,547,104 this year. Visitors from Germany were up 22%; France, 25%; the United Kingdom, 26% and Spain 16%.

Travel to Cuba “for tourist activities continues to be prohibited”, said Hagar Chemali, a spokesperson for the US Treasury Department, which publishes the rules on Cuba travel. But in January, after Barack Obama announced detente with Cuba’s communist government, “we eased the travel regulations”, Chemali said.

The new rules make it easier to get the necessary paperwork, and that has led some Americans to flout the restrictions. While many Americans still travel with expensive, organized “people to people” tours that are approved by the US government, it’s not uncommon to encounter Americans who have traveled to Cuba independently to drink mojitos and head to the beach.

Charter companies flying travelers from the US to Cuba say travelers now need only “self-certify” that their trip falls under a permitted category. “The person calling us needs to tell me, ‘I’m going in support of the Cuban people, or professional research, or a family visit,’” or any one of the 12 allowed categories, said Tessie Aral of ABC Charters. After that, “all they do is sign a certification”.

The federal register states that travelers “must retain specific records related to the authorized travel transactions” for five years, but what those records consist of is not spelled out, and Aral said travel providers are not required to review travelers’ itineraries or receipts.

Bob Guild of Marazul Tours, another charter company, worries that some travelers may be viewing the process of planning a trip to Cuba too casually by claiming that they’re going for a sanctioned purpose when in fact they are going on vacation. But Guild acknowledges that “there’s a disconnect” between what’s on paper and what’s happening. “It’s a foggy land right now,” he said.

Attorney Robert Muse, an expert on the legal aspects of Cuba travel, says “there’s been almost no active enforcement” of the tourism ban under the Obama administration. He added that the increase in US visitors to Cuba is “what the Obama administration wants ... They favor engagement. That’s why they take this liberalized approach to travel”.

The Cuban government did not respond to a request for comment, but tourism minister Manuel Marrero recently said visitors were up by 30% and that Cuba was willing to accept the increase.

As for those rushing to see Cuba “before it changes”, Muse said, they think that in the future “there are going to be Burger Kings on every corner. That’s not going to happen, but people still want to see the end of revolutionary Cuba”.