If you want to avoid chemicals I've heard that using powdered sugar and sprinkling it over all frames/bees will force them into a cleaning process and that knocks the mites off. It won't get any mites in the capped brood so you'd have to do it every few days to be sure to get the majority of mites. You can also use a sugar syrup in a spray bottle to the same effect.
A pro for MAQS is that it isn't absorbed into honey (stays safe for human consumption) and it also penetrates the brood capping to kill the mites in the cells.
A con of the MAQS is that I've read about people who have lost a portion of bees (very young or very old) after treatment, there's a thread on here somewhere of someone who lost their queen after treating with MAQS