Insights of ANN–LM-based Levenberg–Marquardt algorithm for a fractal–fractional Hepatitis-C model incorporating immune response

Background and Objective: This paper’s goal is to investigate a fractal–fractional-order differential mathematical model of Hepatitis C infection dynamics, considering the virus’s two primary mechanisms of transmission, virus-to-cell and cell-to-cell as well as the cure rate of infected cells., both virus to cell and cell to cell, as well as the rate at which infected cells recover. Methods: The Atangana–Toufik Scheme and Artificial Neural Networks (ANNs)-based Levenberg–Marquardt (LM) Algorithm are used to evaluate the four compartments that make up the model: the infected hepatocytes, the vulnerable hepatocytes, the viral burden and the humoral immune response, which is triggered in the host to combat the virus. Results and Conclusions: Error histograms, performance assessments, regression analysis, correlation indices and fitness curves based on the Mean Squared Error (MSE), which ranges from 10[Formula: see text] to 10[Formula: see text], are used to evaluate the LMB-ANN’s accuracy and efficacy. Tables and graphs for four sections are used to further validate the outcomes predicted by ANNs. For these settings, the absolute error between the reference solution and the ANN-predicted outcomes ranges from 10[Formula: see text] to 10[Formula: see text]. Furthermore, the existence and uniqueness of the solution are investigated, and Fixed-Point Theory (FPT) is used to assess stability. Parameters Sensitivity and disease-free equilibrium are also discussed in this study. The quantitatively graphical results demonstrate that the addition of a fractional-order derivative reduces the peak of viral proliferation and minimizes cell damage when therapy is initiated early. However, it takes longer to fully remove the illness.