INVESTIGATING THE SUCCESS OF IVF WITH FRACTIONAL-ORDER MODEL: ANALYSIS AND CASE STUDY

The study aims to identify the factors influencing In Vitro Fertilization (IVF) outcomes at Near East University (NEU) hospital in Northern Cyprus, by linking the different IVF model compartments and using mathematical modeling to simulate the dynamics of the procedure. The proposed model has five compartments, and when compared to classical integer-order models, the fractional-order model under the Caputo sense used in this model provides a more accurate representation of biological mechanisms by accounting for the impact of memory and complicated connections that affect IVF outcomes. The surface plots of each variable illustrates how this variable changes over time at fractional order 0 < κ < 1, indicating stronger memory effects and modeling real life situations. This research shows the simulation of each variable at different fractional-order values and population and how the fractional orders significantly influence the interaction between compartments. The framework’s local and global stability has been achieved, and the uniqueness of its solutions is investigated. The model highlights the significance of clinical strategy optimization, including sperm concentration, egg retention, embryo survival, and transplantation success. This model bridges the gap between mathematical analysis and reproductive health care, facilitating further investigations and clinical utilization. Positive beta Human Chorionic Gonadotropin (bHCG) and live birth based on complete cycles are key indicators of IVF success, reflecting modern clinical practice and promoting safe behavior, which can guide patient counseling and influence public policy.