The Department of Health and Environmental Control shall designate as its agents local health inspectors of incorporated towns or cities for the enforcement of the terms of this article and the rules and regulations issued pursuant thereto within one mile outside the corporate limits of such town or city. Such local health inspectors shall enforce such rules and regulations as may be issued by the Department under the terms of this article. In counties having health units it shall be the duty of such health units to enforce the rules and regulations of the Department in the territory of such counties lying beyond the distance of one mile from the corporate limits of towns or cities having local health inspectors. Provided, that nothing herein shall affect the Richland County board of health from having concurrent jurisdiction with the designated local health inspectors to implement the rules and regulations within one mile of the boundary of a city or town.