I take author-san doesn't know what anemia is, huh. No anime/manga author seems to know either...
Anemia has nothing to do with resting or staying up late, it has to do with poor diet and blood loss, anemia is lack of red blood cells, the most common factor is absence of iron in the blood, can have other causes but they are pretty rare, absence of iron is by far the most common, probably more than 90%, heck, more than 95%, as anemia is a veeeeeeery common sickness. The lack of red blood cells causes less oxygen to be carried around the body, which reduces energy production, which causes tiredness. When the case is not extreme, like severe blood loss, simply eating a metric ton of iron heavy food (like beans, peas, liver, dark gree leaves, etc) should be enough.