Numerical computation of the stochastic hepatitis B model using feed forward neural network and real data

Area of Science:

• Epidemiology
• Computational Biology
• Mathematical Modeling

Background:

• Hepatitis B virus (HBV) poses a significant global health challenge, with complex transmission dynamics influenced by environmental factors, host-pathogen interactions, and vaccination. Accurately modeling HBV spread is crucial for effective control strategies.
• Existing models often struggle to capture the inherent uncertainty and heterogeneity in disease transmission, necessitating advanced analytical frameworks.

Purpose of the Study:

• To develop and validate a novel hybrid framework integrating stochastic differential equations and feed-forward neural networks (FFNNs) for analyzing hepatitis B virus transmission dynamics.
• To accurately capture the complexities and uncertainties associated with HBV spread in heterogeneous environments.
• To assess the model's performance using real hepatitis B case data.

Main Methods:

• Formulation of a stochastic model for HBV transmission incorporating a saturated incidence rate and theoretical analysis for well-posedness, extinction, and persistence.
• Development of a feed-forward neural network (FFNN) trained on real hepatitis B case data to approximate the stochastic model dynamics.
• Hybrid framework combining stochastic simulations and FFNN predictions for enhanced analysis of HBV transmission.

Main Results:

• The stochastic model provides theoretical guarantees for disease dynamics, including conditions for extinction and persistence.
• The FFNN effectively approximates the complex dynamics of the stochastic model when trained on real hepatitis B case data.
• The hybrid framework demonstrated strong agreement between stochastic simulations and neural network predictions, validated by low Mean Squared Error (MSE) and Absolute Error (AE).

Conclusions:

• The proposed hybrid framework offers a robust and effective approach for analyzing hepatitis B virus transmission dynamics, accounting for inherent uncertainties.
• This novel combination of stochastic modeling and neural networks provides a powerful tool for understanding and predicting disease spread in complex epidemiological scenarios.
• The validated framework shows promise for improving public health strategies aimed at controlling and mitigating the impact of hepatitis B globally.