When public welfare demands, the director may order the slaughter or destruction of any animal affected with or exposed to any contagious, infectious, or communicable disease that is affecting or may affect the health of the state's animal population. The director may order destruction of any animal held under quarantine when public welfare demands or the owner of the animal fails or refuses to follow a herd or flock plan. The director shall give a written order directing an animal be destroyed by or under the direction of the state veterinarian.