Thus, we obtain the equation for J$_{i}$ ( t ) as when J$_{i}$ ( t ) at t = 0, we have the solution as The daily purchase intention is defined from J$_{i}$ ( t ) as follows, Thus, we can rewrite the equation (1) to the equation for the purchase intention as the following way. This equation is the base of our mathematical model presented in the next subsection. The number of integrated audience can be calculated using the purchase intention as follows, We extend the purchase intention to the range before the movie release date, because the customer has each purchase intention even before the movie release because of the adver- tisement of the movie. The purchase intention of the individual person will increase rapidly toward the release date of the movie because of the concentrated advertising campaign. Since we pointed out in the previous section that the number of the entry of the blog-writing can be considered as the quasi-revenue, it is interesting to compare the quasi-revenue and the extended purchase intention before the release of the movie. Since the purchase intention of the individual customer increase due to both the adver- tisement and the communication with other persons, we construct a mathematical model for hit phenomena as the following equation. dJ$_{i}$ ( t ) dt = a (1 − J$_{i}$ ( t )) (6) J$_{i}$ ( t ) = 1 − e − at (7) dJ$_{i}$ ( t ) dt = I$_{i}$ ( t ) (8) dI$_{i}$ ( t ) dt = − aI$_{i}$ ( t ) (9) N ( t ) = ∫ t 0 ∑ i I$_{i}$ ( τ ) dτ (10) dI$_{i}$ ( t ) dt = − aI$_{i}$ ( t ) + advertisement + communication (11) 6