All these problems are a result of their biological processes, what we need to do is somehow stop them from engaging in such processes... one tried and true way to do this is to deprive them of food, shelter, and adequate health care- then it becomes- as you put it- a 'self-limiting matter'...

But then, we are already doing that- aren't we....

Perhaps you could team up with this douche...err entrepreneur:
http://www.nydailynews.com/news/national/tech-bro-pens-open-letter-san-francisco-riff-raff-article-1.2535921

I just spent 6 days in San Francisco, the streets were filled with broken and ignored people- it made me mad and disgusted, but not at the victims - I am disgusted at the system and organizations that allow this to happen.

I wonder what dysfunction led to this being such a problem in San Francisco vs other cities...

but if you rather not spend the time and money thinking about and addressing the causes, then this is a cheap solution:

Homeless spikes are all the rage....

Planning on voting republican?