The government of the Bahamas has sent 900 police and military personnel to the islands of Abaco and Grand Bahama, hardest hit by Hurricane Dorian, while taking action to stave off any profiteering by private-sector rescue missions amid signs of chaos in some of the aid operations.

The destruction caused by the hurricane was still unfolding, a week after it landed in the northern reaches of the Bahamas as a category 5 storm.

The government has said at least 43 people have died, but authorities are still trying to reach some areas that were cut off by flooding and debris.

There are reports of several thousand people still missing and also of acute health, hygiene and security concerns fast developing in the Bahamas’ northern islands.

The Bahamian government said 120 Jamaican security personnel arrived on Saturday evening and 100 troops from Trinidad and Tobago were to arrive on Sunday as part of the aid effort.

“Large numbers of security forces” from Britain and the United States are involved in search, rescue and recovery operations, authorities said.

About 250 people who lost their homes in the storm arrived in the Bahamian capital Nassau on Saturday after a 13-hour trip on a government-chartered ferry, joining hundreds of other people from the Abaco and Grand Bahama islands who were desperate to escape harsh conditions there.

Residents of Heritage Community throw out their damaged property after the floods caused by Hurricane Dorian, in Freeport, Grand Bahama, on Sunday. Photograph: Cristóbal Herrera/EPA

Carlen Merizier, 23, said she and her two-year-old son were lucky to be alive. She said “a lot of people died” and that she started praying when her home collapsed in the hurricane.

Other survivors, some with no more than the clothes they left in, also arrived in Florida at the weekend on a cruise ship that went to the islands’ assistance.

Meanwhile, emergency officials in the Bahamas said they have had to “clamp down” on aircraft demanding payment for evacuating displaced people from some of the areas devastated by Hurricane Dorian.

The Bahamian government’s National Emergency Management Agency (Nema) said aviation authorities are aware of reports of “commercial activity” and would revoke flight permission for any aircraft charging fees.

The agency said in a statement on Sunday that no flights are permitted to bill the authorities for evacuations and that consumer protection officials are investigating “incidences of price-gouging”.

A website started by a member of the public in the Bahamas for people unofficially to log missing persons has at least 6,500 names on it and, as of Sunday afternoon, while many have the status “known” recorded next to the name, more names have “unknown” written next to them.

Civil aviation authorities said they were restricting air space over the Abaco islands and Grand Bahama to prevent accidents and ensure only approved aircraft that are providing aid can fly there.

Officials have authorized 200 private planes in the area and say “saturated airspace was creating a volatile situation”.

Phillip Smith, the executive director of the Bahamas Feeding Network, a non-profit organisation, was organising the delivery of 20,000 meals to those most in need in Freeport, on Grand Bahama.

“Just going into the communities here is tough. Seeing kids who haven’t had a drink of water in quite a while, it’s a confronting thing,” he said.

There are fears that patchy remaining water supplies in the damaged areas will be contaminated and survivors are at risk from disease, also with dead bodies yet to be recovered.

The government is scrambling to find shelter for tens of thousands left homeless.

“It’s going to get crazy soon,” Serge Simon, a 39-year-old ice truck driver, told the Associated Press in Freeport on Friday as he waited with his wife and two sons, five months old and four. “There’s no food, no water. There are bodies in the water. People are going to start getting sick.”