Intelligent neural framework for modeling the lifestyle-induced remission in the type 2 diabetes

Diabetes is a chronic disease and a major health concern all over the world, even when made feasible to learn about the root cause of the disease by awareness along with the methods of prevention. Regular exercise and a balanced diet are the best approaches to prevent and manage diabetes. According to recent research, a specific lifestyle adjustment strategy can help patients with diabetes achieve remission and restore normal blood glucose levels. This study examines a mathematical deterministic model that describes the progression of type II diabetes, formulated as a system of ordinary differential equations. Two data-driven modeling approaches are employed to solve this system: a Levenberg–Marquardt-based artificial neural network and a deep neural network implemented using the Keras library. A reference dataset was generated using the fourth-order Runge–Kutta method, and both models were trained and tested. The model accuracy was evaluated using the relative L2 error and relative root mean square error across various activation functions. To test the effectiveness of the model, Gaussian noise of various intensities was added to the data, and Monte Carlo simulations were conducted. The mean relative error provides a statistical measure of the performance. The numerical findings indicate that the Levenberg–Marquardt-based artificial neural network, configured with a distinct architecture and activation function setup, attains a test relative root mean square error in the range of 10−6 to 10−7, compared to 10−4 to 10−5 for the Keras-based model. This demonstrates that the relative root mean square error-based evaluation provides a more reliable and sensitive measure than the relative L2 error, highlighting the superior accuracy and robustness of the Levenberg–Marquardt-based artificial neural network framework under the tested configurations. Monte-Carlo simulations demonstrate the superior resilience and predictive precision of the Levenberg–Marquardt-based artificial neural network model yielding lower relative error values (0.0001–0.0070) compared to the Keras framework (0.0010–0.0053) across all noise levels ranging from 1% to 3%. This superior performance enables the Levenberg–Marquardt-based artificial neural network to consistently outperform the Keras-based model in terms of both predictive accuracy and noise resilience. Furthermore, a comprehensive sensitivity analysis was conducted to quantify the impact of key input parameters on the output dynamics, revealing the most influential factors governing the system behavior. In the proposed framework, pre-diabetes progresses to diabetes, while remission at moderate to severe stages is achieved solely through lifestyle changes without medical treatment.