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Here are a few options:
Even though you keep your mattress covered with sheets and blankets, it can still get dusty and dirty. When you take the sheets off to wash them, spend a few minutes vacuuming your mattress with a hand attachment. It will help those who have allergies and if the mattress happens to get wet, there will then be less dirt to stain it.
If you've had your mattress for a few years and you've never cleaned it, it might be a good idea to take an upholstery cleaner and a sponge to it. These cleaners are safe on both fabrics and skin. Unless you are highly sensitive to cleaners, it should be safe to use and can remove stubborn dust mites from your mattress.
If your mattress has a spot or stain, spray it with a citrus cleaner and let it soak for a few minutes. After a few minutes pass, blot the cleaner out with a clean cloth. You could also use a mild dish detergent. Never rub at the stain or it will just move deeper into the mattress.
Mix one part baking soda and two parts cold water to create a cleaning solution. Apply it to any area of the mattress that needs to be cleaned and let it sit for half an hour. Then, use a damp cold cloth to rinse the solution from the mattress. Dry the area with a towel to take out any leftover moisture.
Get fabric freshening and virus killing sprays and simply spray the mattress down when you take the sheets off. Let it dry for an entire day before you put new sheets on.