Steve Esmond, his teenage sons and the teens' mother fell ill more than two weeks ago in St. John, where they were renting a villa at the Sirenusa resort.
The family has confidence in their medical professionals and is hopeful for a full recovery, according to a statement released Monday from the family's attorney, James Maron.
The teens' mother, Theresa Devine, was treated at a hospital and released, and is in occupational therapy, Maron said.
The U.S. Environmental Protection Agency said Friday that the presence of a pesticide at the rented villa in St. John may have caused
the illnesses, which were reported to the EPA on March 20.
Paramedics were called to the villa, which the family was renting.
Esmond was found unconscious; the boys and their mother were having seizures, Maron said. The lawyer did not say who called the paramedics.
Elias Rodriguez, an EPA spokesman, said the agency's preliminary test results "do show that there was a presence of methyl bromide in the unit where the family was staying."
Exposure to methyl bromide can result in serious health effects, including central nervous system and respiratory system damage, according to the EPA
The use of the pesticide is restricted in the United States because of its acute toxicity. It's not allowed to be used indoors. Only certified professionals are permitted to use it in certain agricultural settings.
In strawberry fields
For example, the pesticide is injected into the soil of some U.S. strawberry fields, said Judith Enck, an EPA regional administrator.
"We trust that the strawberry producers are making sure that there's not excess pesticide residue on strawberries," Enck said. "You definitely want to wash them really good.
"This is a pesticide that's been around for a long time, and ironically because of its impact and damage to the ozone layer, it's being phased out because of the air impacts of this fumigant," Enck added.
Field workers at a Connecticut nursery were poisoned by the chemical in 1990, according to the Journal of Industrial Medicine.
In 2011, warehouse workers in California fell ill after exposed to grapes imported from Chile fumigated with methyl bromide, the U.S. Centers for Disease Control and Prevention said.
Banned in many places
Dr. Sanjay Gupta, CNN's chief medical correspondent, said many parts of the world banned the chemical, a neurotoxin. The agent is to be used only outdoors.
The chemical is also odorless and colorless, Gupta said.
"It's not something that you would have any warning of," Gupta said.
The chemical is often mixed with tear gas so people can be aware of its presence, he added.
The EPA said it is working with local government agencies to investigate whether the family was made ill after a fumigation at the resort on March 18 and whether any environmental regulations or laws were violated.
Enck, the EPA regional administrator, said paramedics were called early on March 20.
Sea Glass Vacations, which acts as a rental agent for several units at Sirenusa, said the unit directly below the one where the family stayed was recently treated for pests, but that the family's unit was not treated.
The company said it licensed an outside company, Terminix, for the pest control services.
On Monday, it ended its contract with Terminix.
In an email to CNN before the termination, a spokesman for Terminix wrote that the company is "committed to performing all work ... in a manner that is safe for our customers, employees, the public and the environment" and is "looking into this matter internally, and cooperating with authorities."
The U.S. Department of Justice has initiated a criminal investigation.
"Many questions remain why an odorless pesticide of this level of toxicity could be manufactured, distributed and applied in a residential area resulting in this family's injuries," Maron said.
The attorney added: "The family is confident that the responsible parties will be brought to justice and held accountable."