Just purchased a house with nightmare tenants

[Harold Valencia]

Last week I closed on a two family house that I purchased directly from the owner, she gave me a good deal with the condition that she would stay in the first floor apartment and pay a reduce rent.  The issue is with the second floor tenant, they've been there for 5 years and never had a rent increase.  The previous owner has mobility problems and hasn't been to the apartment since she rented it 5 years ago.  When I did the inspection prior to closing I found out that the dog they have does its business in one of the bedrooms.  There was fresh pee on the hardwood floors and stains from what appeared years of pee.  I looked at their lease which ends in six months, and the lease states "No pets".  My question is, how can I remove these tenants from my property?  They're destroying the apartment and paying about $600 less then market value for it.  TIA..