The Board of Health shall have jurisdiction in all matters pertaining to the preservation of the health of those in attendance, upon the public and private schools, to which end it is hereby made the duty of said Board of Health: To require that all persons attending said schools either as teachers or pupils shall have complied with the order of the State Board of Health concerning vaccination; to exclude from such schools any person suffering with a contagious or infectious disease, or any person liable to convey such disease among those in attendance, and to require and compel the vaccination of pupils when necessary. (1965 Code)