To clean my toilet brush after use I rinse it off in the bathtub with hot water.
Then I add some bleach to a bucket of hot water in a mop bucket and then sit the toilet brush in the hot water and bleach and let it soak overnight or for a few days as the bleach helps to kill the bacteria that is contained on the toilet brush.
Then after a few days I remove the toilet brush and then rinse the toilet brush off in some more hot water and then place the toilet brush back into the toilet brush holder.
You can also use some vinegar in a bucket of water or spray the toilet brush with some rubbing alcohol to kill the bacteria.
I always just use the bleach though and then I dump the bleach and water down the toilet which also helps to disinfect and clean the toilet as well.