The first patient was confirmed after having been intubated for >= 4 days. On average it takes 9 days from infection to ARDS, which requires intubation, according to a Lancet study. She was confirmed 5 days ago (on Feb 23rd). So she could be infected 9 + 4 + 5 = ~18 days ago.

Since only around 20% of patients require hospitalization, we can estimate there are ~5 infected in her cohort. With doubling time outside China at 5-6 days, that means around 3 doublings: 2^3 * 5 = 40 infected today (Many of them will not show serious symptoms; some who will require admission have not progressed to that stage yet.) So far we have assumed that all hospitalized cases are detected, however.

Some who are hospitalized might still not be detected, since without a test or a CT scan, its symptoms are similar to other viral pneumonia. Let's say infected per detected is a factor of 1.5-4. Very rough estimates: ~60-160 infected in the Bay Area now.

https://www.wired.com/story/community-spread-coronavirus/

https://www.thelancet.com/journals/lancet/article/PIIS0140-6...

Doubling time outside China: https://ncov.r6.no/