A university would like to know whether it is a good idea to start an online distance learning program in addition to the regular on$-$site program. The members of the board would like to gain an understanding of the likely dynamics of the number of online over time. Similar programs elsewhere show that:

Students enroll when entering the program, and unenroll when finishing the program or when quitting. The annual number of students that passes the program is equal to $10\%$ of the total number of online students. Students unenroll due to dissatisfaction with the program. Dissatisfaction is mainly caused by the quality of the teaching. Enrollment is directly proportional to the tuition fee, and is highly dependent on word of mouth advertisement by current and former students. In addition, the more students there are in the online program, the lower the costs per student. Tuition fee is $30\%$ more than the cost per student.

Develop the dynamic model related to this system.