When an order of the council creating a vector control district has been filed in the office of the county auditor of a county in which the district or a part of the district is situated, a three-member board of commissioners of the vector control district must be appointed as provided by this section. Any resident freeholder in the district is eligible for appointment to the board of commissioners thereof. The term of commissioners first appointed must be determined by lot. One commissioner shall hold office for a term of two years, one shall serve for a term of three years, and one shall serve for a term of five years. The term of a commissioner commences on the date of appointment. If the office of a commissioner becomes vacant, the commissioner appointed to fill the vacancy shall serve the unexpired term of the member of the board of commissioners whom the new commissioner replaces. Any vacancy must be filled in the manner provided for original appointments. Appointments to the board of commissioners must be made by the board of county commissioners of the county containing the largest area of the vector control district. Any member of the board of commissioners may be removed upon a majority vote of the board of county commissioners that appoints members for the board of commissioners and the board of commissioners may be dissolved upon a majority vote of the board of county commissioners that appoints the members for the board. The appointing authority shall establish the rate of compensation for commissioners and actual expenses incurred by commissioners may be reimbursed at the official reimbursement rates of the appointing authority.