âThis is going to be frustratingâ: JeffCo health officer on vaccine and limits Vaccine supply does not meet demand (Source: KSLA) By WBRC Staff | February 5, 2021 at 3:25 PM CST - Updated February 5 at 3:25 PM BIRMINGHAM, Ala. (WBRC) - Jefferson County Health Officer Dr. Mark Wilson said the county health department has been preparing and is ready for the expansion of the COVID-19 vaccine starting Monday, February 8. Wilson said there are thousands of people able to get the vaccine and a large number of people who want the vaccine. Right now there is not enough vaccine to fill the need, but health leaders will distribute the vaccine as quickly as they get it.