Bir teknoloji bağımlılık modelinin optimal kontrolü

In this thesis, an epidemiological model is developed to describe the dynamics of technology addiction among individuals. The population is divided into five compartments: Spreaders (S), Light Users (L), Heavy Users (H), Bad Mental (B), and Recovered individuals (R). The transitions between these compartments are modeled by a system of ordinary differential equations, and the evolutionary process of addiction behavior is analyzed mathematically. Following the formulation of the model, an optimal control problem is constructed to reduce the number of addicted individuals and to minimize the cost of intervention strategies. Four control functions are introduced, and the necessary optimality conditions are derived based on classical optimal control theory. For the numerical solution, the Forward-Backward Sweep method is applied. Numerical simulations are conducted to evaluate the effectiveness of the control strategies on the addiction dynamics. The results demonstrate that the application of control strategies significantly improves the system behavior by decreasing the number of addicted individuals and increasing the number of recovered individuals. The findings of this study provide valuable insights for developing effective intervention strategies against technology addiction.