(A) Any dog that has attacked and bitten a person or other animal without provocation or has attempted to bite a person or other animal without provocation shall be deemed a vicious dog.
(B) It shall be unlawful for any person to cause, permit, accompany or be responsible for the presence of any vicious or diseased dog on the streets or public places of the city or allow the dog to run on the premises of another, at any time; unless in addition to other requirements of this chapter the dog shall be securely muzzled to effectively prevent it from biting any person or other animal.