A mathematical model of cinematic box-office dynamics with geographic effects

A new deterministic mathematical model for North American box‐office film grosses is presented. The model may be simplified to a set of non‐linear ordinary differential equations describing the evolution over time of the film's gross and exhibited sites. The novel feature of this work is the inclusion of geography‐based effects to model moviegoer and exhibitor behaviour. Several key regimes are identified, depending on the popularity of the film, as well as how the screens are divided among geographical regions. Analytical results are presented for several relevant cases. Numerical simulations demonstrate close agreement between the model's predictions and actual box‐office data.