When asked how many Cubans are working in Venezuela, minister of foreign affairs Elías Jaua cites the 25,000 medical aid workers in the programme launched by the late president Hugo Chávez, adding "about 1,000 sports trainers and 600 farming technicians". The opposition claims the number is higher, particularly as there are Cuban advisers in all the ministries and state-owned companies.

At the end of February the student leader Gaby Arellano tried to present a petition to the Cuban ambassador in Caracas. "We will not allow Cubans to interfere in our affairs any longer," she said. "We don't want them to go on controlling the media, directing military operations or indoctrinating our children." Teodoro Petkoff, a leftwing opposition figure, is not convinced Havana exerts that much influence. "Such claims play down the responsibility of the Chavistas for what's going on," he says.

Defence specialist Rocío San Miguel believes Cuba really does influence policymakers in Venezuela. She recalls the way Chávez's illness was managed, his hospitalisation in Havana clothed in secrecy, and the transfer of power to Nicolás Maduro (pictured), who was educated in Cuba. "Cuban officers attend strategic planning meetings for the armed forces," she says, basing her claim on insider sources.

"It's not a myth, it's the reality," says General Raúl Baduel, minister of defence under Chávez and now in custody at the Ramo Verde military prison. The Cubans have modernised the intelligence services, both the Sebin (Bolivarian National Intelligence Service) that reports directly to the president, and military intelligence. They also set up a special unit to protect the head of state.

Furthermore Cubans have computerised Venezuela's public records, giving them control over the issue of identity papers and voter registration. They have representatives in the ports and airports, as well as supervising foreign nationals. They took part in purchases of military equipment and work on the Maracaibo airbase.

"All Cuban 'internationalists' have had military training and must, if required, fulfil combat duties," San Miguel asserts. "Cubans form an information network which keeps Havana up-to-date on shifts in public opinion," says political observer Carlos Romero.

Chilean president Salvador Allende, right, alongside Cuban president Fidel Castro during his visit to Chile in 1972. Photograph: Corbis

The Cuban regime, says Romero, wants to avoid three "worst-case scenarios", which have in the past led to the downfall of governments sympathetic to Havana. The first was the overthrow of Chile's President Salvador Allende in 1973. This explains its efforts to placate the Venezuelan military. The national guard, which has been in the frontline quelling demonstrations, has been awarded bonuses for its good offices.

The second case was Grenada in 1983, where Cuban influence was undermined by the regime's mistakes, prior to invasion by American troops. Havana is consequently determined to shore up Maduro's authority and end the dispute with his rival, Captain Diosdado Cabello, who is head of the National Assembly and deputy leader.

The third scenario to avoid is an election in the throes of an economic crisis, as occurred in Nicaragua in 1990. So the priority in Venezuela is to stop inflation and end the shortages that are sapping popular support for the Chavistas. An election is due next year.

Havana is clearly keen to maintain the status quo. But killing demonstrators, imprisoning political opponents and members of parliament – making martyrs of them in the process – is a far cry from the low-intensity repression that Raúl Castro has inflicted on Cuban dissidents since he took over from his brother Fidel. Nor is Cuba in the habit of engaging in dialogue with the opposition, as Maduro did on 10 April, broadcast live on television.

It remains to be seen whether the thousands of Cubans scattered all over Venezuela will fan the flames of radical revolt or help restore calm.

This article appeared in Guardian Weekly, which incorporates material from Le Monde

• This article was amended on 28 May 2014 to correct a reference to the 1983 American invasion of Grenada. An earlier version of the article mistakenly referred to Granada.