Although source material author Paul Theroux and nephew Justin Theroux are close, Paul had nothing to do with Justin's casting for the part. It was only after Justin booked the part that he got to call his uncle to surprise him with the news.
Original book was written by Paul Theroux and turned into a movie. 35 years later it was being remade into a series starring his nephew, Justin Theroux.
Influences for Paul Theroux on Allie Fox were Huckleberry Finn's father, Jim Jones, and [founder of Mormonism] Joseph Smith. There were also elements of Paul's own father in the character which is coincidental since that means it was also Justin Theroux's grandfather. Justin recalled in one interview that his grandfather used to take him dumpster diving.
The Foxes were not on the run from the police in the novel or the movie, but they are in the TV series.
Interesting contrasts between the 2021 series and the 1986 movie. Harrison Ford as Allie is more manic where as Justin Theroux is more calculating. Helen Mirren as Margot is more compliant and doting on Allie than Melissa George who is more feisty and independent. The family dynamic is quite different - whilst River Phoenix and Gabriel Bateman were both 15 playing Charlie, River is the oldest of 4 kids so is closer, and initially more obedient, to his dad whereas Gabriel is the baby of only 2 kids with Logan Polish playing 18 year old Dina who is also feisty and independent. The 2021 Fox family have many more dramatic trials to traverse but the 1986 Foxes live more in the wild. The 1986 movie attempts to tell the story in a single 2 hour movie whereas the modern version is two 7 episode series with a 2 year gap between filming allowing the children to mature more.