From the Albert Einstein Healthcare Network:
For the claim:
A Dutch research team conducted a small, preliminary study that provides some indirect support for the old myth. They found that the subjects’ immune systems responded differently under the conditions of feeding versus starvation.
While these are intriguing findings, they say little about how a person suffering from a cold or a fever can expect to actually feel when fed or starved. Although the study was small and inconclusive, the idea that food consumption may have a short-lived effect on the immune system is a new one, as previous studies have focused on more long-term effects.
Against the claim:
Current medical opinion puts the “feed a cold, starve a fever” maxim in the same category as other medical advice from the Middle Ages–false and maybe even dangerous!
An infection–particularly one associated with fevers– is no time to deny your body the nutrients and fluids it needs. Like any bodily system, the immune system requires energy to function properly.
Whether you’re thirsty or not, drink plenty of fluids. And, if you’re hungry–eat!
From Duke Health:
Although a few small-scale studies
have suggested that “feed a cold,
starve a fever” loosely represents
sound medical advice, Duke medical
experts caution against putting too
much faith in the adage.
From the European
Food Information Council:
You do not need to do either. Instead
it's better to follow your appetite,
although if you are sweating a lot
[...] it is really
important to increase your fluid
intake to avoid becoming dehydrated.
The stress of illness can increase protein demands.
Other important nutrients needed for the production of "germ-gobbling" cells in the immune system are zinc (in seafood and red meat) plus folic acid and pro-vitamin A (beta carotene) in broccoli, spinach and carrots.
More Sources that say the claim has little merit: