My cat has tapeworms but has never had fleas!

I just found out my cat has tapeworms. It is too late to take him to the vet but i read they get them from fleas and he never has had fleas! He is strictly an indoor cat and i am a clean freak so there are no fleas in my house. How dangerous are they to me? What can i do in the meantime to make it safer? and How long after being treated will they go away?