I’ll be comparing it to other films below but I think it all starts with Romero’s work—sociopolitical entertainment in this specific mode
The neglectful father is a fund manager, starts the film off as entirely selfish—both his daughter and the greater humanity are victims (he’s making a move in the market that is going to have repercussions that will harm the general populace (he uses lemming in the text) which is a metaphor for the movie).
Certainly 28 Days Later from Danny Boyle an influence in the genre of note, I think Bong Joon-Ho’s Snowpiercer here (2013) too as we’re dealing with a class divide and the evil portion (the deplorably selfish executive here leading the charge) in the front of the train
I also think Wolfgang Petersen’s Das Boot (1981) is a relevant text. Train to Busan uses the cramped quarters of the train (a vast majority of the film and relevant action are on the train) to great effect
Slice of life cast of characters like Grand Hotel or Stagecoach all forced together- the pregnant woman, the selfish fund manager, the grandma, the hobo, the athlete, the corporate jerk— it all boils down to there being two types of people and that’s the central theme— the selfish and selfless and it’s very well-articulated throughout to great narrative intrigue.
The film flies– engaging—relentless action but never needless or tiresome
In a few places there’s a nice use of slow-motion and the silhouette falling off the train at the end is a very beautiful shot as is the tunnel shot of the two survivors emerging