Not all that closely in my opinion. The similarities with the book would be Lord John gets measles, Jamie takes Willie away, and Willie is a spoiled brat.
-Young Ian was there and figures out Willie is Jamie's son. Those are two big changes, and comes up in later story lines if they get that far, but now it can't really.
-No Murtaugh, obviously. So him being there and knowing about Jamie and Willie is astronomically different. As is their arguing.
-Willie doesn't recognize Jamie as Mac, at least not at this point. So that's different and all of the angsty conversations around that are new.
-Pretty sure Jamie doesn't give Claire a new ring.
-As far as I remember, all of the stuff with the Native Americans is show only. So Jamie yelling out Willie is his son totally threw me until I realized they were going to have Willie believe he was just saying that to save him.
All I really want from this change of keeping Murtaugh alive is to see him meet Bree!