Advanced Mathematical Models & Applications

This paper is an effort towards a novel approach for prediction of In-Vitro Fertilization (IVF) success rate by depicting the treatment process as a mathematical model and applying the concept of artificial neural network (ANN). In this study, a mathematical model comprising seven compartments including birth and failure of the process or death of the foetus at any stage. Also, the existence and uniqueness of the solution were presented by using Picard’s theorem to establish that the equations of the model are continuous, satisfy the Lipschitz condition, and are bounded, and the reproduction number R0 has been computed using the next-generation matrix technique. The local stability has been investigated where the system is stable when R₀ > 1. Additionally, an ANN architecture has been constructed in order to investigate the interaction between success rate per cycle of IVF and the age of the mother, with few other significant contributors. Furthermore, a sample dataset was generated to train, validate and test the performance of the neural model, and the evaluation was done based on metrics such as Root Mean Squared Error (RMSE) and Coefficient of Determination (R₂). We obtained an R₂ value of 0.94, indicating a very high correlation between the predicted and actual outcome. Several visualizations support this comprehensive analysis of maternal age and IVF success using scatter plots, line plots, and box plots. Ultimately, the end result reveals that ANN can predict IVF success by paying attention to critical factors in maternal age. It could help healthcare providers to better make decisions and set proper expectations for patients.