(A) Every dog or cat owner, harborer or person having the custody, control, possession of any dog or cat shall keep such dog or cat confined to the premises and property of the dog or cat owner, harborer or custodian, except as hereinafter provided.
(B) No dog or cat owner, harborer or person having the custody, control of or possession of any dog or cat, shall permit, allow or suffer such dog or cat:
(1) To run or be at large as hereinbefore defined; or
(2) To go about or on the premises or property of any other person within the city without the permission of such other person.