With my prior experience I'm looking at this from an EMS lenses... I'm going to give you the pros and cons I see with kicking him out...
Pros: You'll be able to update the place and get a tenant who is potential cleaner, and it would be able to raise rent rates.
Cons: He looks like he has a disability (from the wear marks on the floor) so I'm not sure cleaning is the highest priority for him. This place is probably within easy access to doctors and family for him. Is he living off of social security? If he pays you consistently that's one less tenant that you have to worry about when it comes to turn over.
It doesn't look like it would be too difficult to renovate.
Personally I would let him stay, but if he's laxing so much that it's a detriment to his health (and/or property, like are the floor boards falling in because of filth), call the police and ask what needs to be done to perform a health and comfort check (welfare check).
