Isn't their illness just dohyun and the kid's.... like why is the father going thru such l...

Probably because his father ir trying to develop the drug that could be either a vaccine or the cure itself and who could be the perfect test subject ? Dohyun. Since he have the illness already, why bother troubling himself and finding others when he have his son at his disposal albeit the said son is force through this. Then when they finish the drug, he's father could make it public ( since it's mention before that it's illegal and could only be bought underground ) he can sell it and get both and fame. At this point this is a far fetch but possible theory of mine hahaha