What can I do to get rid of bugs in my violin?

My sisters and I have two violins and a viola. Recently, the chin rests of all three instruments have had small bugs on them. The bugs are real tiny and look like white ants/termites, but my brother says that they are too small to be termites.

We tried dismantling the chin rest and spraying the cork with insecticide. However, the bugs are still there!

At first, we noticed only about two or three bugs on each chin rest. Just today, we checked again and there were a whole lot more crawling around! Strangely, the bugs are only on the chin rest and no where else.

Another thing we noticed today was that the chin rests were a little dusty, coated with something like fine saw dust. I am worried that the bugs are eating our instruments.

Am I the first person to experience bugs living on my violin?

Please advise me on what I can do. I am getting rather desperate, because I dare not play my violin now.

Thank you for your help.