| Abstract: |
| Hepatitis B is a significant global health issue with serious consequences like liver cancer, cirrhosis, and liver failure. The virus spreads through contact with infected blood, body fluids, or contaminated needles. With over 350 million chronic carriers and about 800,000 deaths annually, primarily from liver cancer and cirrhosis, it remains a major global threat. Despite advanced preventive treatments, including effective vaccination programs, the risk of chronic Hepatitis B virus infection persists.
The dynamics of the spread of the Hepatitis B virus can be modeled mathematically. Epidemiological models are often formulated as systems of non-linear differential equations. These models can be discretized using methods like Euler and Runge-Kutta, but these can lead to undesirable behaviors such as incorrect equilibrium points or numerical instabilities. To address these issues, a non-standard finite difference scheme can be constructed. In this study, a Hepatitis B virus model will be discussed, and a non-standard finite difference scheme for this system will be established. It will be shown that the discrete system provides dynamically consistent results with the continuous model, regardless of the time step size $h$, regarding the positivity and boundedness of solutions, equilibrium points, basic reproduction number, and stability behavior. Numerical simulations will support theoretical results. |
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