The Dallas County health department offered its best solution Wednesday to an impossible problem: how to distribute 10,700 doses of H1N1 flu vaccine in a county with hundreds of thousands of people who need the vaccine and can't find it.

The county will start by offering the vaccine to children between 6 months and 18 years old who have chronic medical conditions. A phone bank will open this morning for people to make appointments for Friday, Monday or Tuesday.

A walk-in clinic for members of the high-risk groups – children, young adults and others with chronic illnesses – will be Wednesday.

The one spot of good news is that the level of swine flu infection in Dallas County has dropped dramatically from a few weeks ago, county medical director John Carlo said.

"The epidemic is lessening, so the risk is lowering," he said.

And as has been true since the H1N1 virus appeared in the spring, most people who catch the illness recover after a few crummy days.

On the other hand, a few get very sick. Carlo urged those at highest risk for severe illness to get vaccinated when possible. The flu has not vanished, and nobody can predict whether the virus will return for another round of widespread illness.

Underscoring that point, the county confirmed its 14th H1N1-related death Wednesday, a 35-year-old man with significant underlying medical conditions. Officials released no other details, citing patient privacy.

The vaccination programs announced Wednesday are only for Dallas County residents and are intended for people who have no insurance. They will be held at the county's health department headquarters building on Stemmons Freeway.

Tarrant County will hold its first walk-in vaccination clinic Friday. That clinic is intended to serve only pregnant women and children with chronic diseases.

Dallas County health officials assume they will see large crowds next week. Health department director Zachary Thompson said he was caught between the need to serve the uninsured and the unexpected shortage of vaccine.

"We cannot provide all the vaccines that are needed for the residents of Dallas County," he said.

Here are the numbers that overwhelm the county's current supply of vaccine:

•Federal health officials estimate that about 60 percent of the population fits into one of the high-risk groups, Carlo said. The population in Dallas County is probably similar to the national average, which means the risk groups here could total about 1.4 million residents.

•Pregnant women are at particular risk. More than 38,000 babies are delivered each year in Dallas County.

•Children between six months and 18 years old are another high-risk group, totaling about 670,000 people in Dallas County. Carlo said about 5 percent of children have asthma and a smaller percentage have other illnesses that increase the risk. Taking only the 5 percent, that's more than 33,000 people.

•The health department says it intends to serve only those with no insurance, which is about 23 percent of the population. That would mean there could be more than 300,000 people at risk who lack insurance. If only 5 percent of this population comes to get vaccinated, that's still more than 15,000 people.

While the county now has only 10,700 doses, more could be delivered before the clinic opens next week.

But even the insured may decide this is their best option. Carlo said that about 60,000 doses had been delivered to private providers as of Wednesday. But many doctors have little or no vaccine available.

That puts the health officials in a tough spot.

"We aren't going to turn anybody away if they are a Dallas County resident," Thompson said. "We should not be police in this process. It should be an honor system."

Officials, however, will do some policing. People must provide proof of Dallas County residency or risk being turned away from the Dallas County health department clinic. And visitors to the Tarrant County clinic will need to fill out a form verifying that they meet that county's criteria before they can get a shot.

The state health department decides where the vaccine goes. The state is spreading the available doses geographically, finding the providers serving the highest-risk populations, and alternating weekly between large and small practices, spokeswoman Carrie Williams said.

But there aren't nearly enough doses available yet to meet the demand. The federal Centers for Disease Control and Prevention said this week that production of the vaccine is speeding up but remains well behind earlier predictions.

"We know the urgency is there now," Carlo said. "Ultimately, there will be plenty of vaccine."

Where: Dallas County health department, 2377 N. Stemmons Freeway, Dallas

When: Appointment-only on Friday, Monday and Tuesday. Walk-in clinic on Wednesday from 8 a.m. to 4 p.m. or until vaccine runs out.

Who: The first three days are only for children 6 months to 18 years old with chronic illnesses. Wednesday is for all risk groups: pregnant women, children and young adults, caregivers of infants, and adults 25-64 with chronic illnesses. The intent is to serve people with no medical insurance.

To qualify: Must have photo ID or other proof of Dallas County residency

To make an appointment: Call 214-819-6001 beginning at 8 a.m. today.