modeling and optimization of the number of graduates in a multi-specialization study program

Consider a study program which offers a number of specializations, and requires all students to be enrolled in exactly one specialization at any given time. we construct a continuous mathematical model governing the time evolution of the number of students enrolled in each of the program's specializations. using the model, we further construct an optimization problem describing the search of an intervention strategy which maximizes the program's total number of graduates, along with a framework for sensitivity analysis. we discretize the constructs accordingly, and employ a coordinate-descent method to solve the optimization problem numerically in two simulated scenarios involving two and four specializations, respectively, describing the results' practical implications.