Very good question. I guess dipping it in alcohol? You don't want to expose it to heat as the bristles would probably melt. The alcohol may do some damage too depending on the material that the bristles are made from.
What brush do you have? If I have the same and it's not a user, I'll try the alcohol thing and see how I get on.
Just wondering why you'd need a sterile brush ? Are you operating on a human with it ?
Because the way I see it your entire bathroom , hands , face , sink for sure , countertop , shave brush , razor , bathroom rug and any magazines (crapper reading material) are covered with germs . Don't sweat it . My house is full of germs too . As I'd suspect everyones is . Just shave with it and rinse with hot water . Haven't heard of any humans that died while using a shaving brush .