Originally one member of the district board of health shall be appointed for one year, one member for two years, one member for three years, one member for four years, and one member for five years. Upon the termination of the term of appointment, members shall thereafter be appointed for a term of five years. Vacancies which occur on the district board of health shall be filled for the unexpired portion of the term of the vacated member by appointment as provided in § 34-3-13.
SDCL 34-3-14