Every house carries quite a bit of matter and pollutants within the air. Illnesses and allergies often get stemmed from this fact. During cold seasons, closed windows make it worse in your home so it is especially important at those times.
Using air purifiers is a big way to help cut back on those air pollutants and irritants. Choose from floor models and table models with many features like fan speed, oscillation, etc. No matter what you purchase, it will help to reduce allergens and pollutants.
As an alternative or addition, you can place fans in your windows to exhaust those annoying pollutants. This is a very effective way to purify the air, assuming you have other windows open to bring fresh air in. You may have to clean the screens periodically, but you will see what went out the window and you will have fresher air!
Your vacuum cleaner may pull up dirt and debris well, but how does it handle the air return. A cheaper vacuum tends to stir up the contaminated air. It floats around in your home and then begins to find a new resting place after a while. HEPA vacuum cleaners help a bit more, but cheaper versions let air escape through gaps and cracks back into your home. Some have a higher level of suction to effectively clean with ease, but also kick around the air so it floats in your home.
A home that is air contaminant free is basically nonexistent, but can be controlled to a comforting level.