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Scientists have come up with strong immunological evidence for why you should always feed a cold.
Writing in Physiological and Biochemical Zoology, Lynn Martin and her colleagues found that dieting deer mice, given 30% less to eat, had far fewer memory B cells, which make protective antibodies, than mice allowed to eat normally.
According to Martin, "30% restriction in food intake doesn't affect body mass and only minimally reduces activity in deer mice, but it eliminates the long-term immune protection provided by antibodies." This means that the results could have profound implications for human health and they certainly fit with previous findings including trials in which malnourished subjects given measles vaccines responded very poorly compared to counterparts who were better-fed, and infections that are more frequent and tend to be chronic in malnourished children.
Significantly, malnourished and self-neglecting individuals with weakened immune systems are also more likely to promote the spread of infectious diseases, like TB, because the bugs are able to persist in these people for longer, and are often present at higher levels making the patients more infectious.
So your grandmother was part right when she told you, feed a cold - but definitely don't starve a fever.