There is some good information regarding cleaning and disinfecting mattresses if you click the related link I added to your question.
Disinfect
u cant clean a thick down mattress
Run it through the washing machine set on "hot".
dry cleaners
You can disinfect it by wiping it down with a disinfectant wipe.
Clorox products can both clean and disinfect surfaces. They are designed to remove dirt and grime while also killing bacteria, viruses, and other germs.
You wash the item with clean, hot soapy water then rinse or wipe clean afterwards.
Yes, there are some mattress pads that are dry clean only, but they are usually specialzed pads.
Removing cat dander from a mattress is simple. First vacuum the mattress then steam clean it and set it out to dry.
Alcohol
With a wet paper towl and rubbing alcohal to disinfect it
Clean it with water and disinfect it (hydrogen peroxide is good).