A multi-layer computational neural network approach for solving stochastic within-host Chikungunya model with an adaptive immune response

Viral infections represent a leading cause of morbidity and mortality globally. Despite significant advancements in vaccine development and antiviral therapies, these infections continue to pose substantial public health challenges, necessitating further investigation. This research introduces a novel numerical computing procedure for stochastic within-host Chikungunya virus transmission model using a multi-layer neural network and spectral collocation method. Initially, we investigate a numerical scheme for the proposed model using the Legendre Spectral Collocation Method (LSCM). The reproduction number of the model is determined and the stability of the stochastic model is proven using Itô formula. The model dynamics are further analyzed graphically, to illustrate the impact of key parameters under stochasticity. Furthermore, the numerical simulation of the proposed stochastic model is presented using a feedforward neural network (FFNN), and its accuracy is validated by comparing the results with those obtained from the LSCM. The reliability of the scheme is assessed using various performance metrics, including regression analysis, mean squared error (MSE), error histograms and state transition evaluations. Moreover, a comparison of the absolute errors between the spectral method and FFNN is conducted across all state variables of the model, demonstrating their relative accuracy and effectiveness. The low error and near-perfect regression validate the reliability of the FFNN in simulating biological processes and ensuring accurate predictions of disease progression. The proposed numerical procedure can be efficiently extended to simulate complex real-world systems beyond epidemic models.