ANN computing framework for modeling and predicting the dynamics of fractional order hepatitis C virus model

In this paper, we developed a framework that describes the transmission of a hepatitis C model with fractional and machine learning approach for analysis and numerical outcome. The model consists of four groups: viral load, susceptible hepatocytes, infected hepatocytes, and the humoral immune response that the host triggers to fight the virus. Biological feasibility of the model, such as positivity, uniqueness solution through fixed point results. The fractional-order power law kernel solution function was used to set up the numerical simulation. Using data collected by Fractional Order Differential Equations (FODEs) with a fractional order power law kernel solution function, MATLAB was implemented to perform the simulations in question. This is accomplished through the application of the Bayesian Regularization Backpropagation Artificial Neural Network (BRB-ANN) intelligent computing technique. The data set for training the BRB-ANNs is created using Fractional Order Differential Equations (FODEs). The Bayesian Regularization Method with Backpropagation Artificial Neural Nets (BRB-ANNs), the fractional-order hepatitis C virus (FOHCV) model’s precision and effectiveness were significantly improved. The effectiveness of the proposed strategies is evidenced by achieving exceptionally low absolute errors ranging from ( 1 0 − 3 ) to ( 1 0 − 9 ) , minimal Mean Square Error (MSE) values between ( 1 0 − 7 ) and ( 1 0 − 10 ) , and an almost perfect coefficient of determination ( R 2 ≈ 0 . 999 ) . Furthermore, the error histograms (Er.Hgs), ranging from ( − 9 . 4 × 1 0 − 10 ) to ( − 4 . 12 × 1 0 − 6 ) , along with the corresponding time series plots (TSP), further validate the precision and reliability of the developed models. Dynamically and graphically, demonstrations indicate the achievement of AI with BRB-ANNs compared to the standard solution, and 3D Lorenz curves for FOHCV are analyzed. These results support the theoretical observation of Hepatitis C disease epidemics and the prediction of disease patterns, which in turn assists policy-makers in designing public health policies.