The board shall protect the health of the domestic animals and nontraditional livestock of this state, shall determine and employ the most efficient and practical means for the prevention, suppression, control, and eradication of dangerous, contagious, and infectious diseases among the domestic animals and nontraditional livestock of this state, and shall prevent the escape and release of an animal injurious to or competitive with agriculture, horticulture, forestry, wild animals, and other natural resource interests. For the purpose of preventing the escape and release of an animal injurious to or competitive with agriculture, horticulture, forestry, wild animals, and other natural resource interests, the board may, by rule, quarantine any such animal, cause any such animal to be killed, regulate or prohibit the arrival in or departure from this state of any such animal, and at the cost of the owner thereof, the board may detain any animal found to be in violation of any rule or prohibition. Any matter relating to the health and welfare of domestic animals and nontraditional livestock and not specifically assigned by statute to another entity is deemed to be within the authority of the board. The board may make rules to carry into effect the purposes of this chapter and other duties prescribed in this title.