A Sinusoidal-Based Mathematical Model for Psychotherapy Effects in Bipolar Disorder Type 2 Patients - Indah Nursuprianah; Nursanti Anggriani; Nuning Nuraini; Yudi Rosandi (CAUCHY: Jurnal Matematika Murni dan Aplikasi, 2025)
Bipolar Disorder (BD) is a mental disorder characterized by recurrent manic and depressive episodes. This study aims to build a mathematical model that models mood changes in BD type 2 before and after psychotherapy. Daily mood data were collected for more than 3 months from one BD patient, then divided into seven terms of 14 days each. The analysis was carried out through a sinusoidal function fitting process and numerical simulation based on the Van der Pol differential equation. The results showed that before psychotherapy, the mood amplitude reached 1.99632, the frequency was 0.4926, and the moment of inertia was 4.121081. After undergoing routine psychotherapy 9 times, the amplitude decreased to 0.635, the frequency increased to 1.052, and the moment of inertia decreased to 0.903584. The average mood was controlled at 6.492, within the normal mood range. The decrease in amplitude and moment of inertia indicated that BD mood became more stable and less easily affected by the environment, while the increase in frequency indicated a faster recovery of emotional rhythm. Conclusion: Routine psychotherapy is effective in quantitatively stabilizing the mood of BD type 2.