In the last calendar quarter of each year, the members of the State Board of Health shall meet and elect a chairperson of the board from the members and such other officers, including a vice-chairperson and a secretary, as the board deems necessary. In case of the death, resignation, or other permanent absence of the chairperson of the board, the vice-chairperson shall assume the office of chairperson and the members of the board at the next regular meeting of the board, or at a special meeting of the board pursuant to a call signed by five members of which the other members shall have at least three days’ notice, shall elect a new chairperson of the board from the members and such other new officers as the board deems necessary.