| Summary: | The research aims to understand and study type 1 diabetes and its response to treatment using a mathematical model. We employ a novel method that combines the Shehu transformation with the Akbari–Ganji approach and the Padé approximation to derive approximate solutions for this model. The research findings convincingly show the effectiveness of the method used. The results show a positive impact of the investigated treatment on individuals with type 1 diabetes. Strong agreement is observed between the results obtained from this model's solutions and those of previous studies, confirming the accuracy and reliability of the simulation method employed. This method is considered a successful simulation technique for future studies, enhancing our understanding of the effects of treatments on individuals with type 1 diabetes. From a practical standpoint, the study's results can offer valuable insights to healthcare professionals, enabling them to make more informed decisions regarding treatment strategies. These insights have the potential to optimize treatment plans, potentially leading to improved health outcomes for patients. Furthermore, this research paves the way for further advanced studies in the field of medical modeling and simulation.
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