(A) As used in sections 5579.04 to 5579.08 of the Revised Code, "noxious weed" means shatter cane (Sorghum bicolor), Russian thistle (Salsola kali var. tenuifolia), or any plant designated a prohibited noxious weed by the director of agriculture.
(B) A board of county commissioners, a board of township trustees, or the street commissioners of a municipal corporation, having control of and being charged with the duty of repairing macadamized, graveled, or improved roads, and county engineers, township road superintendents, and the street commissioners of each municipal corporation, between the first and twentieth days of June, the first and twentieth days of August, and, if necessary, the first and twentieth days of September of each year or whenever necessary to prevent or eliminate a safety hazard, shall destroy all brush, briers, burrs, vines, noxious weeds, and, until June 1, 1996, multiflora rose, growing within the limits of a county or township road or improved, graveled, or macadamized road, street, or alley within their jurisdiction.