A city of the primary class may provide for the destruction and removal of weeds and worthless vegetation growing upon any lot, lots, or lands within the corporate limits of such city or within its extraterritorial zoning jurisdiction or upon the streets and alleys abutting upon any lot, lots, or lands, and such city may require the owner or owners of such lot, lots, or lands to destroy and remove such weeds and worthless vegetation therefrom and from the streets and alleys abutting thereon. If, after five days' notice by publication, by certified United States mail, or by the conspicuous posting of the notice on the lot or land upon which the nuisance exists, the owner or owners fail, neglect, or refuse to destroy or remove the nuisance, the city, through its proper officers, shall destroy and remove the nuisance, or cause the nuisance to be destroyed or removed, from the lot, lots, or lands and streets and alleys abutting thereon and shall assess the cost thereof against such lot, lots, or lands as a special assessment.