Much of the work was done by convicted drug abusers living in a network of halfway houses who can earn early release through public service, Dr. Rullán said.
Many of the island’s hundreds of schools have no screens or air-conditioning. Since high school girls account for about 20 percent of all pregnancies here, officials plan to screen the windows to keep out mosquitoes.
That alone is a big job. “That means measuring each window,” Dr. Rullán said. “And what are you going to do about doors if you have 50 kids running in and out?”
As a first step, the public school dress code has been changed so girls can wear pants, and teachers are supposed to give mosquito repellent to all girls.
In the island’s 109 cemeteries and its many auto junkyards and public dumps, mosquito-control teams have begun spraying pesticides that kill the insect’s larvae. But the work is never-ending because rain washes the pesticides away.
Moreover, the island is dotted with hundreds of abandoned homes with water-collecting birdbaths and pools. Puerto Rico has 500,000 septic tanks, each of which can produce up to 1,500 mosquitoes a day if left unsealed.
Teams cannot enter an abandoned property or screen a septic tank when the owner is absent, “so we’re asking for a new law letting us enter,” Dr. Rullán said.
The ideal, he said, would be to spray every property within 150 yards — the distance a mosquito normally travels — of every pregnant woman’s home.
The island’s birthrate is about 10 per 1,000 women, and nearly 100 women a day become pregnant here. Just finding them all would be a gargantuan task.
A Hunt for Solutions
Other mosquito-control efforts are even less effective.
Highly visible fogging by trucks is what most people associate with government mosquito-fighting. But permethrin, the insecticidal fogger used for years, may actually be useless.
Tests at several sites have found that its ability to kill mosquitoes has significantly faded, so the island will have to choose a new pesticide and retrain workers to use it.
Even with the right chemical, the impact of fogging is dubious. Aedes mosquitoes typically hatch in gardens and slip into houses to hide in closets and under beds. When the spray trucks go by, many people close their windows, locking themselves in with the enemy.
Aedes mosquitoes are “sip feeders” and bite several times for each blood meal. The number required to make an infection likely for one member of a household is as few as three mosquitoes, experts have found.
Moreover, by a “very inconvenient coincidence,” the Environmental Protection Agency has effectively banned the chemical used here to kill juvenile mosquitoes, Audrey Lenhart, a C.D.C. entomologist, noted. The chemical, temephos, has been in use since 1965 and definitely works, she said. But it is not very profitable, so when the agency demanded safety data costing about $3 million to gather, the manufacturers decided instead to quit making it.
Puerto Rico still has a nine-month supply, Dr. Lenhart said, and the E.P.A. may issue an emergency use permit for more.
Mosquitoes are not the only mode of Zika transmission, however. Health authorities here have also been forced to grapple with an unexpected twist: the discovery that sex spreads the virus.
The government has frozen the price of condoms, threatening stores with fines of up to $10,000 if they raise the cost. (It did the same for repellent and window screens.)
At nutrition clinics, teachers like Ms. Morales have struggled to explain, as they hand out condoms, why the partners even of pregnant women should wear them.
In a radio interview in January, Puerto Rico’s health secretary, Dr. Ana Ríus, advised women to delay pregnancy altogether, if possible, until the epidemic is over.
But local radio commentators accused her of alarmism, and Roberto González, archbishop of the Catholic Church, publicly criticized the government’s condom distribution plans. Instead, he counseled people to “practice self-discipline, which we believe is the only rational attitude and faith.”
It will be many months before officials know whether their efforts have slowed the advance of the Zika virus.
“Come October, when the babies start being born,” Dr. Rullán said, “I’ll know if we acted in time or not.”