As swine flu continues to spread across universities nationwide, Yale may not have enough vaccine supplies on hand to protect all of its students.

Yale will receive its first shipment of the H1N1 vaccine from the New Haven Health Department “sometime next week,” Yale University Health Services Director Paul Genecin said Thursday. But because of high demand across the city, the University may initially receive fewer vaccines than it requested.

“We’re asking for as many [vaccines] as the state will give us,” Genecin said.

New Haven Health Department Assistant Director Kenneth Rubano said that because children between the ages of two to four are most vulnerable to swine flu, most of the city’s first H1N1 vaccine shipment will head to local pediatricians. But as more shipments arrive weekly from the state government, everyone who wants a vaccine will ultimately get one, said William Gerrish, a spokesman for the Connecticut Department of Public Health.

Gov. M. Jodi Rell announced Thursday that 20,000 doses of the H1N1 nasal spray vaccine have arrived. Another 20,000 doses of both the shot and the nasal spray should arrive next week, Rell added.

So far, city authorities have documented 400 swine flu cases in New Haven. But there have probably been over 3,000 unconfirmed cases, Rubano said. According to the Center for Disease Control Web site, symptoms of swine flu in adults include shortness of breath, chest pain, sudden dizziness and severe vomiting. People who have any of these symptoms, Rubano said, should stay home and isolate themselves.

Seven Yale students interviewed were divided on whether they would head to YUHS to get the H1N1 vaccine.

Because many of her friends have had the swine flu, Claude De Jocas ’12 said, getting the vaccine would be a “wise idea.”

Another student, Ben Schenkel ’12, said he would get the shot — only if everyone who was at higher risk than himself of contracting the flu had gotten the vaccine first.

Some students said it didn’t matter to them if they received the vaccine. Shuli Hervitz ’11 said she would not make the trek up to 17 Hillhouse Ave. just for the swine flu vaccine. Ella Dershowitz ’12 said if she hasn’t had the flu yet, she probably won’t contract it any time soon.

According to CDC figures, the federal government has purchased 250 million doses of the H1N1 vaccine at a cost of approximately $1 billion.

The Connecticut Department of Public Health began a program in late August to recruit private providers such as Yale to provide the H1N1 vaccine when it became available. It is now the responsibility of the 50 providers to order vaccines from the New Haven Health Department each week. The New Haven Health Department then forwards the requests to the Connecticut Department of Public Health, who in turn decide based on patient demographics how much of their federal government allotted vaccines will go to each provider.