The thing I've learnt is you cannot manage other people's behaviour, only your own. It can be frustrating or worrying but I just ensure I am doing what I feel is the right thing to do for me (whilst respecting others). Some people don't seem to social distance so I just move rather than get cross.

So I think the best course of action is to move away from this person or work from home. He cannot (and should not) be penalised for his asthma, its unfortunate that he has a cough and I get why its made you worry, but he's explained and you have to accept that I think.