Mathematical Analysis of Autonomous and Nonautonomous Hepatitis B Virus Transmission Models
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arXiv
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866909609707438080 |
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| author | Alsammani, Abdallah |
| author_facet | Alsammani, Abdallah |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_08210 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Mathematical Analysis of Autonomous and Nonautonomous Hepatitis B Virus Transmission Models Alsammani, Abdallah Dynamical Systems 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. |
| title | Mathematical Analysis of Autonomous and Nonautonomous Hepatitis B Virus Transmission Models |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2305.08210 |