Well, I don't know if this would be the health department recommended way, but my dad always carried a comb in his pocket. He also used either Brylcream or Q. E. D., both were forerunners of hair jell. They probably replaced mineral oil and bear grease. But to clean his comb he would take mom's straw broom that she used to sweep the floor, squeeze several of the straws together to make a sort of brush, and use that to clean the comb. Run it under a little hot water in the sink to get rid of anything loose that is left and good to go.

Me, I normally use a toothbrush (not the one I use on my teeth). Just don't tell your wife if you use hers.