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<p>The Hepatitis B virus is a major global health threat, causing chronic liver infection, cirrhosis, and cancer. This paper presents a novel understanding of Hepatitis B virus dynamics using a stochastic epidemic model that incorporates essential real factors associated with the disease, including virus-to-cell and cell-to-cell transmission, and environmental variability represented by Gaussian white noise. We initially demonstrate the existence of a unique global positive solution for the system. Our primary analytical finding demonstrates the existence of an ergodic stationary distribution when the stochastic threshold satisfies <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathbf{R^{s}_{0}} &gt; 1\)</EquationSource> </InlineEquation>. In contrast, we demonstrate that the disease is on the extinction track when <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\mathbf{R^{s}} &lt; 1\)</EquationSource> </InlineEquation>. The theoretical results are rigorously confirmed by two complementary methods: comprehensive numerical simulations and an advanced deep learning framework. This system utilises a Levenberg-Marquardt trained neural network, attaining great accuracy compared to Euler-Maruyama reference solutions, as evidenced by the convergence, evaluation, and distribution of error, regression analysis, detailed curve fitting, and an approaching-zero performance measure. This study presents a comprehensive framework that highlights the significant influence of multiple transmission pathways and environmental noise on infection dynamics, providing essential insights for enhancing HBV control techniques.</p>

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Neural network assisted stability exploration of a stochastic Hepatitis B model incorporating dual transmission routes and immune response

  • 期刊论文

  • 发表日期：

    2026年2月3日

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  • Anwarud Din

摘要

The Hepatitis B virus is a major global health threat, causing chronic liver infection, cirrhosis, and cancer. This paper presents a novel understanding of Hepatitis B virus dynamics using a stochastic epidemic model that incorporates essential real factors associated with the disease, including virus-to-cell and cell-to-cell transmission, and environmental variability represented by Gaussian white noise. We initially demonstrate the existence of a unique global positive solution for the system. Our primary analytical finding demonstrates the existence of an ergodic stationary distribution when the stochastic threshold satisfies \(\mathbf{R^{s}_{0}} > 1\) . In contrast, we demonstrate that the disease is on the extinction track when \(\mathbf{R^{s}} < 1\) . The theoretical results are rigorously confirmed by two complementary methods: comprehensive numerical simulations and an advanced deep learning framework. This system utilises a Levenberg-Marquardt trained neural network, attaining great accuracy compared to Euler-Maruyama reference solutions, as evidenced by the convergence, evaluation, and distribution of error, regression analysis, detailed curve fitting, and an approaching-zero performance measure. This study presents a comprehensive framework that highlights the significant influence of multiple transmission pathways and environmental noise on infection dynamics, providing essential insights for enhancing HBV control techniques.