Katsuki had ended up sick in a stupid manner, really— In the more colder days of Autumn, he wandered off without proper warmer clothing, and that got him dealing with a strong fever now.

He warned Izuku not to get close to him, that he might catch the flu too.

Did the nerd listen? Nope.

Both of them were sick and Izuku was only caring about his boyfriend's health, and not about his own too.