The scene where Alex Cross pays the kidnapper by throwing the thermos containing the ransom from the window of a transit train is taken from James Patterson's novel "Roses Are Red", which starred Alex Cross investigating another of his "best enemies", Kyle Craig, aka "The Mastermind".
This story takes place over the course of a few days. In the novel that the film is based on, the story takes place over the course of around two years. Also, in the book, Alex Cross is 38 years old with two kids, where as in the film he is in his mid to late fifties.
Michael Moriarty plays the father of the kidnapped girl named 'Megan'. Moriarty previously played the part of the stepfather ('Hull Barret') of a girl also named 'Megan' in the 1985 feature film 'Pale Rider' with Clint Eastwood.
In the book the Secret Service is protecting the young boy from the school and Alex Cross is forced onto the case not drawn in. Also there is no female partner like in the beginning of the movie but a partner and best friend since he was 9.
The trivia items below may give away important plot points.
Substantial changes were made from the book on which the movie is based. In the books, the Gary Soneji story arc continues for four books, and he dies under entirely different circumstances. Also, there are two kids kidnapped in the book, one of which dies in the process, which results in Jezzie Flannigan's execution via lethal injection.