A differential equation model of North American cinematic box-office dynamics

A new mathematical model is presented for the box-office dynamicsof a motion picture released in North America. Though previouswork on this problem has usually involved probabilistic methods,the new model for describing cumulative box-office gross usesa continuous-time, differential-equation approach. This model,which consists of a system of three nonlinear, coupled, ordinarydifferential equations, incorporates the effects of marketingand advertising expenses, audience reaction, critical reviews,and previous box-office behavior, among other factors. Analyticalasymptotic results are presented for various parameter regimes.In the general case, the model must be solved numerically. Numericalsimulations are tested against actual revenue data from severalrecent movies to analyse the model's accuracy. An algorithmfor practical usage of the model is presented.