Maybe give him immunity support supplements before he goes? I know this isn't the same but I ALWAYS get sick on a flight unless I take something before I fly. EmergenC or Airborne? Elderberry supplements are good too. 

How old are the collective kids?  Is there anything about the skid's life that might make them more prone to exposure?  larger school? younger age?  Ex's house has other younger kids that pass it along?

Certainly your spouse should be teaching their child about proper hygiene so that they learn to wash hands and not share things without cleaning etc..  

Otherwise, unless it's something that should be seen by a DR... like recurrent strep... you may need to just be more aware on your end on how to keep the kids separated when one of them is ill. 

As a child.. the sick kid was mostly subject to staying in the room and resting.. meals were brought to them.  They were not supposed to be going around infecting the household.  Maybe wellness checks when the child arrives.. taking temps etc?

In the end, it may just end up being an annoying situation.. and if the child has a current KNOWN illness, I personally think it's better for the kid to stay in the sick bed they already are lying in vs making them relocate when feeling funky.