They reproduce by shedding a link from the end of their long bodies. This link crawls out the cat's anus, and sheds hundreds of eggs. These eggs are injested by flea larvae, and the cycles continues. Humans may get these tapeworms too, but only if they eat infected fleas. Cats with tapeworms should be dewormed by a veterinarian.
Cats can get tapeworms from eating mice.
If your cat catches a mouse it is best to take the prize away from it. There are tiny, parasitic worms that can live in a cat's stomach. These worms cause frequent vomiting. Many people fear catching a protozoan disease, Toxoplasmosis, from cats. This disease can cause illness in the human, but more seriously, can cause birth defects in the unborn.