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arXiv · 2305.08210

Mathematical Analysis of Autonomous and Nonautonomous Hepatitis B Virus Transmission Models

Abdallah Alsammani
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Abstract

This study presents an improved mathematical model for Hepatitis B Virus (HBV) transmission dynamics by investigating autonomous and nonautonomous cases. The novel model incorporates the effects of medical treatment, allowing for a more comprehensive understanding of HBV transmission and potential control measures. Our analysis involves verifying unique solutions' existence, ensuring solutions' positivity over time, and conducting a stability analysis at the equilibrium points. Both local and global stability are discussed; for local stability, we use the Jacobian matrix and the basic reproduction number, $R_0$. For global stability, we construct a Lyapunov function and derive necessary and sufficient conditions for stability in our models, establishing a connection between these conditions and $R_0$. Numerical simulations substantiate our analytical findings, offering valuable insights into HBV transmission dynamics and the effectiveness of different interventions. This study advances our understanding of Hepatitis B Virus (HBV) transmission dynamics by presenting an enhanced mathematical model that considers both autonomous and nonautonomous cases.

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BibTeXRIS

Abdallah Alsammani. 2023-05-14. Mathematical Analysis of Autonomous and Nonautonomous Hepatitis B Virus Transmission Models. https://doi.org/10.1007/978-3-031-37108-0_21

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