So will UT4 be free upon release, or will be be under continuous community development?
Both. It's free now and will be free upon release, and it will have continuous development by community mappers and modders. I'm under the impression that they will always be updating the game in various ways, as needed.
To the point, what's the business model behind this?
That's hard to say. It may be, "Draw attention to Unreal Engine 4," or "Serve as an example of what you can do with Unreal Engine 4." Epic has a small team of developers working on the project, so if it loses money or if the business model does not work out, it might not be that big of a deal.
I think they're hoping to make money from the "Marketplace" where mappers and modders can sell maps and mods. It seems unlikely that maps will be sold except for single player campaigns, such as a remake of the original Unreal. The money may be in non-obligatory cosmetic items such as funny hats and weapon skins. It's also possible that a team of modders might create a new game type and charge for it.