There are effervescent tablets that are used for disinfecting, much like ones used for dentures. They only needed to be added to warm water, and you just need to soak the top of the toothbrush in the solution for no longer than 10 minutes. You may talk to your dentist in Annapolis MD to ask which disinfecting tablets are suitable for toothbrushes.
There may be reasons why sanitizing toothbrushes seems logical. However, keeping a brush clean by running it under warm water will also remove the food and toothpaste remaining in the bristles. Afterwards, letting it air dry without touching other bristles will help.