It is sometimes recommended that you “feed a fever”, but there are no human studies examining whether eating more or less improves recovery from an influenza infection (a common cause of fever). Nonetheless, a small amount of research on mice suggests being adequately-fed is worthwhile when dealing with a flu.
A 2017 study looked at whether increasing the food intake of mice would be protective against infection with a strain of influenza A (H1N1). Following infection, the animals naturally ate less (as is common during illness) and many died within 30 days. However, mice who were force-fed an extra 1/5th of their usual calorie intake were more likely to survive the virus.[1] Conversely, research on mice who were energy restricted (e.g., fed a diet with similar amounts of micronutrient but 40% fewer calories) found these animals were more prone to dying following influenza infection.[2] Furthermore, increasing the food intake of these calorie restricted mice leading up to when they were infected partially reversed their viral susceptibility.[2] That being said, all of these studies involved mice infected with very high doses of influenza virus. As a result, the effect of food intake on flu recovery in humans remains uncertain.