A multi-layer neural network approach for the stability analysis of the Hepatitis B model

Area of Science:

• Epidemiology
• Mathematical Biology
• Computational Science

Background:

• Hepatitis B virus (HBV) infection is a major global health concern.
• HBV poses a significant risk, with potential progression from acute to chronic infection.
• Understanding HBV dynamics is crucial for effective public health strategies.

Purpose of the Study:

• To develop and analyze a novel dynamical system for Hepatitis B virus infection.
• To incorporate asymptomatic carriers, vaccination, and treatment strategies into the model.
• To assess the impact of interventions on HBV transmission dynamics.

Main Methods:

• Utilized a system of differential equations to model HBV dynamics.
• Calculated the basic reproduction number (R0) for disease prediction.
• Employed Deep Neural Networks (DNNs) for enhanced model accuracy and prediction.
• Applied Lyapunov functions to confirm global stability of the model.
• Conducted rigorous testing, validation, and training of DNNs.

Main Results:

• The model highlights the critical role of vaccination and early treatment in mitigating HBV spread.
• DNNs demonstrated high accuracy in predicting system behavior across various conditions.
• Convergence studies, error analysis, and regression confirmed the reliability of the DNN approach.
• Identified optimal curves fitting target solutions with minimal residual errors.

Conclusions:

• Vaccination and early treatment are essential public health tools for controlling and potentially eradicating Hepatitis B.
• Deep Neural Networks are a powerful technique for improving accuracy in epidemiological modeling.
• The developed dynamical system provides valuable insights into HBV infection dynamics and intervention effectiveness.