Each county and city shall establish and maintain a local department of health that shall be headed by a local health director. Each such local health director shall (i) be a physician licensed to practice medicine in the Commonwealth, (ii) possess a master’s or doctoral degree in the area of public health and have at least three years of professional experience in a full-time position in either a public health agency or public health-related position, or (iii) be otherwise qualified for the position as determined by the Commissioner. If a local health director is not a physician licensed to practice medicine and there is no licensed physician on staff, the local health director shall enter into a consulting agreement with a licensed physician to execute prescribing duties, consult on clinical matters, and perform all other duties as requested.