Can a bunny catch the sniffles from a carpet that another sick bunny used frequently 2 or 3 months ago?

I just got a Black holland lop buck, i have only a few places to let him run around in my house. the specific area in question which i use a playpen as a fence was also used by my previous rabbit who was very sick and i'm worried he might catch it from playing there. also the old rabbit peed/pood there alot those areas are the ones he sniffs at