SAN RAFAEL (KPIX) — This week it became increasingly clear that the limited supply of coronavirus vaccine will be an ongoing problem for weeks and, perhaps, months.

In San Francisco, 3.6 percent of residents have received at least one dose of vaccine. In Contra Costa County, 6.7 percent of those 16 and older have received at least one dose. In Marin County, the number is somewhere in between.

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“It worked very well, very well organized,” said Barbara Eaton, Saturday, on her way out of the Marin Civic Center. “Everyone was very kind and caring.”

As of about 3 p.m., Eaton joined the ranks of the vaccinated — 4.9 percent of the county’s population, according to a newly-launched dashboard.

“It’s a frustration at every level,” said Marin Public Health Officer Dr. Matt Willis. “For our residents, public health, our hospitals.”

The frustration Willis is describing is shared across the Bay Area and so is the main obstacle to scaling up these numbers, no matter where you live.

“We don’t know any given day how many doses are headed our way,” Willis explained. “It’s very hard to plan and schedule appointments when you don’t know what you’re going to have.”

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That’s why Marin and several other counties are getting more refined in their approach, focusing more on those 75 and older.

“We have heard from the Biden administration they will at least offer us more clarity in terms of what we can expect in the coming weeks and months with regards to doses,” Willis said.

The Biden administration is proposing $20 billion for logistical help to expand vaccination capacity.

“Those things are really going to help,” said UC Berkeley professor Dr. John Swartzberg. “But it’s going to take a while for the dollars to translate into trained people, sites and all the other difficulties in getting these problems lined up.”

So this is what the rate of growth might look like for a while as we are caught in the limits of both logistics and supply.

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“We were kind of hoping the new administration would sort of open the vaults, and find lots of boxes of vaccine that had been distributed,” Willis said. “That’s not the case, so I think we need to set our expectations.”