During a crisis like this, when hygiene is so critical, it is more important than ever to avoid contamination and germ spread. It is best practice for everyone in your household to use a different toothbrush and store each of these brushes separate from one another.
You should always rinse and clean your toothbrush before and after every use. This will remove potential contamination from other objects or products in your bathroom. Toothbrushes are prone to accumulating bacteria, but a thorough rinse should alleviate this. Additionally, using a mouthwash regularly could help to stop the spread of COVID-19 because of its bacteria-killing properties.