I would like to ask about toothbrush problem. I use the same toothbrush after meat and diary products. Small parts of the food, even though I clean the toothbrush, may stay on it. And even though it probably cannot be seen as cooking (temperature of used water is below 45C/115F) though toothbrush may come under the definition of kvishah if it is not used for 24 hours. What is the halachic opinion on this ? Is my toothbrush still kosher ?

The custom is to use the same toothbrush after both, meat and milk meals; same as false teeth.