A novel numerical framework for stochastic tuberculosis modeling with treatment via neural network and spectral method
摘要
Tuberculosis has a serious health concern and global challenge due to its prolonged treatment duration, complex response to therapies and less cure rates. In this study, we propose a novel feedforward intelligent framework that combines neural networks with spectral methods to solve a stochastic TB transmission model incorporating treatment. The model integrates stochastic perturbations to capture the inherent uncertainties in TB spread. A higher-order spectral collocation technique is used to discretize the system, providing enhanced numerical stability and precision. This is further coupled with a supervised feedforward neural network that efficiently approximates the stochastic solution space, enabling accurate simulation of TB dynamics under randomness. A detail simulation is performed to validate the proposed scheme, revealing significant improvements in convergence rate, accuracy, and robustness over traditional numerical methods. Furthermore, the robustness of the proposed neural network-based scheme is evaluated using multiple performance metrics, including regression analysis, mean squared error (MSE), error histograms, and state transition assessments. Finally, the accuracy and effectiveness of the developed stochastic computational method, integrated with neural networks, are validated by comparing the results with those obtained using the conventional spectral collocation method. The robustness of the proposed methodology is assessed by comparing the outputs with the best validation performance, approximately 10−6, and low absolute errors varying from 10−3 to 10−6. The stochastic intelligent computing surrogate presented in this study can be effectively implemented to investigate the complex dynamics of epidemiological models with randomness.