In the past five weeks, manufacturers have shipped 1 million doses to New Jersey — enough to vaccinate nearly one in eight people. But it’s far short of what an exasperated, worried public demands. Every day, more than 800 people call the state H1N1 hotline, and nearly all of them are looking for help finding a swine flu shot. About 20,000 have called since the hotline opened Oct. 6, state Health Department spokeswoman Donna Leusner said. Figuring out where to get a shot is no simple matter. Those navigating the “find a flu shot” database on the department’s website last week saw about half of the counties didn’t have clinics scheduled. And some places will offer the shots only to pregnant women or youngsters because the vaccine comes in different forms.

“I understand the vaccine is difficult to produce and to get. But I find it interesting the way it’s been disseminated,’’ said Kelly Brakewood of Tewksbury, who waited for weeks for the Hunterdon County Health Department to hold its first flu clinic so she could vaccinate her 15-year-old son and 12-year-old daughter.

“I normally don’t get them vaccinated (for seasonal flu) but I have been doing a lot of reading,” she said. “It’s really affecting kids. That makes me nervous.’’

Using the flu shot database on the state health department’s website last week, Brakewood found a clinic in Morris County and made an appointment. (Hunterdon County has since announced it will hold its first clinic today.)

Top federal officials blame the lag in filling vaccine orders on the slow and outmoded way the vaccine is produced. But state officials say distributing the swine flu vaccine is fraught with its own complications that have at times ground the process to a crawl.

There are 1,033 physicians, health officers, retail pharmacy operators, hospital and clinic administrators, and private companies who requested the vaccine, Leusner said. They have as many as six different formulations to choose from, depending on the age and health of the people they are trying to protect.

The U.S. Centers for Disease Control and Prevention says pregnant women are among the most vulnerable to the virus, but they cannot use the nasal spray form of the vaccine — what was widely available in the first few weeks — because it contains the live virus.

Some OB/GYNS and pediatricians have ordered mercury-free shots, which are in very short supply. Meanwhile, children ranging in age from six months to 17 years require different amounts of vaccine to ensure their protection.

The slow production complicated by the special orders has created a backlog of orders for 400,000 doses in New Jersey, state epidemiologist Tina Tan said. And until that backlog clears, Tan said no new orders will be submitted.

“The issue now is making sure everybody who had placed orders get those orders first, before we continue to allow people to place more, or we could perpetuate the back-order problem,’’ Tan said.

David Papi, the chief health officer in Middlesex County, said he was surprised and disappointed to hear the state’s strategy.

“Middlesex County is the second largest county in the state, behind Bergen County. “You would think logically we would get a bigger allotment,’’ Papi said. “I have hundreds of thousands of people who need to get done. From my standpoint, it’s not looking better.’’

Anybody checking the flu shot locator database midway through last week would have found no public clinics scheduled in 11 of the state’s 21 counties. The database changes every day, and by Friday, two more counties had added clinic dates.

Papi acknowledged his department held a swine flu vaccine clinic Friday at the fire academy in Sayreville that did not make the state’s list. “There’s so many things to do it’s possible we’re just not getting the clinics listed’’ on the state website. He urged people to consult the county’s website for the most up-to-date information.

At the state’s request, county health departments are taking the lead in accepting the swine flu vaccine and holding clinics to benefit many communities, Tan said.

Of the 1,075,200 doses shipped to New Jersey, 559,900 went to county and local health departments, 251,800 went to physicians’ offices; 105,200 went to hospitals; and 73,800 went to private companies and state and municipal government agencies. The rest went to federally qualified health clinics, colleges, retail pharmacies and nursing homes and home health care agencies, according to the state health department.

The same manufacturing delays bogging down production of the H1N1 vaccine have also slowed down the development of seasonal flu shots because they are made the same way, state and federal health officials have said.

The find-a-flu-shot database provides information on clinics dispensing both seasonal and H1N1 vaccine, according to the state website.

Manufacturers and health officials said at some point there will be enough swine flu vaccine for everybody who wants it.

To consult the state flu shot locator database, go to http://www.state.nj.us/health/flu/findflushot.shtml. The hotline number is (866) 321-9571. Star Ledger.