(2) One of the trustees, so designated in such original appointment, shall hold office until the second Tuesday of January following his appointment, one until the second Tuesday of the second January following his appointment, two until the second Tuesday of the third January following their appointment, one until the second Tuesday of the fourth January following his appointment, and two until the second Tuesday of the fifth January from their appointment. Thereafter, the term of office of each appointee shall be five years from the end of the preceding term. At the expiration of the term of each of said trustees, the office shall be filled by appointment of the board of county commissioners.

(3) In those counties having a population of less than three thousand, the board of public hospital trustees shall consist of five citizens at large having the same requirements with reference to their fitness for such office as all other counties. One of said trustees, so designated in such original appointment, shall hold office until the second Tuesday of January following his appointment, one until the second Tuesday of the second January following his appointment, one until the second Tuesday of the third January following his appointment, one until the second Tuesday of the fourth January following his appointment, and one until the second Tuesday of the fifth January following his appointment. The term of office and the method of filling vacancies shall be the same as for all other counties.