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Encasing mattresses is one of many good parts of a solution, but it doesn't get rid of the infestation. There are going to be other bugs away from the mattress, hiding nearby. What mattress covers are good at is entombing the sometimes large number of bed bugs that can live on a mattress. And because the covers tend to be uniform in color and don't have a lot of seams that the bugs can hide in, it's easier to see the insects.
Bed bugs occur around the world. Before the 1950s about 30% of houses in the United States had bedbugs. Rates of infestations in developed countries, while decreasing from the 1930s to the 1980s, have increased dramatically since the 1980s. Before the 1980s they were common in the developing world but rare in the developed world. The increase in the developed world may have been caused by increased international travel, resistance to insecticides, and the use of new pest-control methods that do not affect bed bugs.
All of the stages of bed bugs are visible, at least if you don't need reading glasses and you have a sufficient amount of light. So if you're looking closely enough, you can even see bugs in the nymphal first instar stage. A fecal spot, for its part, can be as large as a bed bug itself in terms of the area it covers. The spots are basically digested blood, so most are dark in color. On a white mattress, they stand out pretty well.
Unlike those of other insects, bed bug bites may sometimes appear in tight lines of multiple, small, red marks where multiple bed bugs have fed along an exposed area. Bed bug bites can cause itchiness. Initially, a victim may detect a slight burning sensation. The burning area then develops red bumps, known as papules or wheals (rash). In extreme cases, bites may swell dramatically or turn into blister-like skin inflammations.