As discussed above, a vacuum cleaner with HEPA filters is what you need if you have allergy sufferers, keeping the microscopic irritants sealed inside the dust bin. However, the big issue is what happens when you empty a vacuum.
For bagless cleaners, emptying has to be done with care, as opening the bin can create a cloud of dust, releasing smaller particles back into the air, causing issues for those with allergies.
Bagged vacuum cleaners have an extra level of protection, as the bags act as both additional filters to prevent particle escape, but you also remove and throw away the dirt without exposing it to fresh air. Look for a cleaner that has self-sealing bags for the best results.
As such, bagged vacuum cleaners are often easier to deal with for households where members are very sensitive to allergens.
That doesn’t make bagless cleaners a poor choice, though: just be careful how and where you empty the vacuum’s bin. To prevent the spreading of allergens, a vacuum bin should be ejected either down, directly into a larger internal bin or, for additional safety, emptied in the same way into an outside bin.