<p>Hepatitis C virus (HCV) and Hepatitis B virus (HBV) infections are leading causes of liver-related diseases, including cirrhosis, hepatitis, and hepatocellular carcinoma (HCC) worldwide. This study presents a two-part framework for hepatitis management: a classifier for disease detection and a fractional-order model for progression prediction. For detection, we developed the Jacobian-Regularized Network (JRN)–a neural classifier with stability regularization, batch normalization, residual connections, and dropout. Trained on 130 patients with 11 clinical features, the JRN achieved an accuracy of 0.846, an ROC-AUC of 0.976, and perfect recall (1.0). Aspartate aminotransferase (AST) was the most important predictor, followed by patient age and creatinine level. Jacobian stability metrics declined during training, confirming improved model robustness. For progression, we developed a fractional-order compartmental model using the Caputo-Fabrizio derivative to capture memory-dependent HBV-HCC dynamics. Stability analysis and equilibrium conditions were characterized using the basic reproduction number <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$R_0$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>R</mi> <mn>0</mn> </msub> </math></EquationSource> </InlineEquation>. A Multi-Layer Perceptron-Fractional Physics-Informed Neural Network (MLP-FracPINN) combined patient data with physical constraints on the network dynamics. Sensitivity analysis identified immune response time (<InlineEquation ID="IEq2"> <EquationSource Format="TEX">$\tau _1$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>τ</mi> <mn>1</mn> </msub> </math></EquationSource> </InlineEquation>) and infection rate (<InlineEquation ID="IEq3"> <EquationSource Format="TEX">$\beta $</EquationSource> <EquationSource Format="MATHML"><math> <mi>β</mi> </math></EquationSource> </InlineEquation>) as critical intervention targets. The model quantifies that 8.9% of chronically infected individuals progress to cirrhosis, and 5.2% of cirrhotic patients develop early HCC. This integrated framework provides clinicians with validated tools for early hepatitis detection and personalized prognosis of disease progression.</p>

Jacobian-regularized network for hepatitis disease detection and fractional-order modeling for hepatitis progression with vaccination

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发表日期：

2026年6月22日

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Vetrivel Muthupandi,
Arul Joseph Gnanaprakasam

摘要

Hepatitis C virus (HCV) and Hepatitis B virus (HBV) infections are leading causes of liver-related diseases, including cirrhosis, hepatitis, and hepatocellular carcinoma (HCC) worldwide. This study presents a two-part framework for hepatitis management: a classifier for disease detection and a fractional-order model for progression prediction. For detection, we developed the Jacobian-Regularized Network (JRN)–a neural classifier with stability regularization, batch normalization, residual connections, and dropout. Trained on 130 patients with 11 clinical features, the JRN achieved an accuracy of 0.846, an ROC-AUC of 0.976, and perfect recall (1.0). Aspartate aminotransferase (AST) was the most important predictor, followed by patient age and creatinine level. Jacobian stability metrics declined during training, confirming improved model robustness. For progression, we developed a fractional-order compartmental model using the Caputo-Fabrizio derivative to capture memory-dependent HBV-HCC dynamics. Stability analysis and equilibrium conditions were characterized using the basic reproduction number $R_0$ $R_{0}$ . A Multi-Layer Perceptron-Fractional Physics-Informed Neural Network (MLP-FracPINN) combined patient data with physical constraints on the network dynamics. Sensitivity analysis identified immune response time ( $\tau _1$ $τ_{1}$ ) and infection rate ( $\beta $ $β$ ) as critical intervention targets. The model quantifies that 8.9% of chronically infected individuals progress to cirrhosis, and 5.2% of cirrhotic patients develop early HCC. This integrated framework provides clinicians with validated tools for early hepatitis detection and personalized prognosis of disease progression.