Health officials confirmed Tuesday that the 12-year-old Lincoln girl who died over the weekend did have swine flu, and revealed that a middle-aged woman died Monday of a suspected case.

Skyla J. Reposa-Alves, a seventh grader at Lincoln Middle School, was the second Rhode Island child within a week to succumb to the virus, which is now widespread around the state. Nationwide, at least 114 children have died of swine flu, including 19 last week. Two-thirds had chronic health problems.

Skyla was generally healthy but had a rare condition that might have increased her risk, said Health Director David R. Gifford. The middle-aged woman, who has not been identified, had several underlying health conditions.

“We’re seeing a lot of people get ill over a very short period of time,” Gifford said. “We’re seeing the same virus that we saw in the spring, but a lot more people are getting sick. How serious the disease is hasn’t changed.”

Meanwhile, turnout for the first 10 school-based vaccination clinics on Monday met the Health Department’s expectations, with three-quarters of the students getting swine-flu shots. Participation ranged from 41 percent at St. James School in Lincoln to 87 percent at the Wilbur & McMahon School in Little Compton.

“Overall, they went very well — better than expected,” Gifford said of the clinics. Two children were taken to the hospital to make sure they were not having a reaction to the vaccine after they said they had a “scratchy throat,” Gifford said. They were fine.

“Some kids felt like they were going to pass out,” Gifford said. “One kid was crying and threw up on the injector.” Otherwise, the clinics were “very calm and very orderly,” he said.

Clinics are scheduled at elementary schools every day through Friday. Gifford said that he expected to have enough vaccine — 25,000 doses — to carry out next week’s school-based clinics as scheduled.

Additionally, more doses of vaccine are being made available to pregnant women, young children, pediatric emergency-room workers and 1,000 extremely high-risk children who are patients of Hasbro Children’s Hospital specialty clinics.

The state Department of Education reported that 29 schools on Monday had more than 20 percent of students absent, one barometer of the flu’s spread. The 29 schools were in 15 cities and towns. Providence and Warwick each had six schools with absentee rates above 20 percent.

Skyla, the Lincoln girl, died on Saturday after going to the hospital the day before with difficulty breathing. She was placed on a ventilator, but her lungs filled with fluid. Skyla was born with Prader-Willi syndrome, a rare chromosomal disorder that causes a chronic feeling of hunger, a metabolism that uses drastically fewer calories than normal and low muscle tone. Children with Prader-Willi tend to be obese and often have learning problems.

It is not clear whether Prader-Willi made Skyla more vulnerable to swine flu. The Prader-Willi Association’s Web site urges people to get vaccinated, but notes that people with the disorder have recovered from swine flu infections “with no serious consequences.”

Some studies suggest that obesity might increase the risk of complications from swine flu, but obese people are not on the federal government’s list of priority groups for vaccination.

Skyla’s funeral will be held Friday at 8:30 a.m. at the Bellows-Falso Funeral Chapel, 160 River Rd., Lincoln. Her family asks that contributions be made to the Prader-Willi Syndrome Association of New England, the Providence Animal Rescue League or Hasbro Children’s Hospital intensive care unit. An online guest book can be found at www.bellowsfh.com

Word of Skyla’s death did not prompt large numbers of parents to keep children home from school, said Lincoln School Supt. Georgia Fortunato. The district absenteeism rate was just over 10 percent on Monday, higher than normal for this time of year, but comparable with other schools during the swine-flu epidemic.

But parents did turn out in force for the swine-flu vaccination clinic Tuesday at the Northern Lincoln Elementary School. When the clinic started at 4:10 p.m., a long line of parents and children were already waiting.

Sue Alves, who came with her children, J’Nesa, 7, and Dominic, 10, recalled that she had been “a little concerned” about possible side effects from the flu shot but finally decided over the weekend it would be safer for everyone if they got the shot. She said Skyla’s death clinched her decision.

In addition to Skyla, two other children have died of swine flu in Rhode Island. A teenage girl who was a student at the Meeting Street School and who had underlying health conditions died in June. Victoria Sousa, of Bristol, an athletic 12-year-old in apparent good health, died of swine flu on Oct. 26.

Adults have also died of swine flu. A woman between 40 and 60 died July 3 and an elderly man died Aug. 4. Both had underlying health conditions and lived in Providence County. The woman who died Monday is considered a likely case, but swine flu has not yet been confirmed. She was admitted to the hospital over the weekend. A resident of Providence County, she had several underlying illnesses and was between 40 and 50 years old.

As the virus spreads, more vaccine is also moving into Rhode Island, according to health director Gifford. In addition to the school-based clinics, Gifford announced that the following doses of vaccine are being distributed:

•3,500 doses to obstetricians for pregnant patients (in addition to 3,000 that went out last week).

•4,500 “baby” flu vaccine doses to pediatricians; these doses are formulated for children ages 6 months to 2 years old.

•About 2,000 shots to pediatricians for high-risk children ages 2 to 5.

•200 doses of vaccine for children of all ages who have undergone transplants at Hasbro Children’s Hospital. An additional 800 doses for children with cystic fibrosis, cancer, congenital heart disease or other extremely serious conditions will be going to the specialty clinics at Hasbro Children’s Hospital over the next week.

•Some 1,700 doses of nasal-spray vaccine to health-care workers who take care of children in emergency rooms.

With reports from Richard C. Dujardin