I would say that the common cold is not worth modeling. You could have a cold, or not, and it wouldn't affect your ability to climb a rope or swing a sword to the same degree as having Strength 12 compared to Strength 14.
If it was a really bad flu, then I would apply the Poisoned condition. I think the general rules for overcoming illness would fall under the downtime rules, where you get to make a check every three days to try and shake off Mummy Rot or whatever. I would probably give a lower DC to trying to shake that flu than I would to shaking off Mummy Rot.