Positivity preserving numerical method for epidemic model of hepatitis B disease dynamic with delay factor - Rehman, Muhammad Aziz ur; Kazim, Muhammad; Ahmed, Nauman; Raza, Ali; Rafiq, Muhammad; Akgul, Ali; Zakarya, Mohammed (Elsevier, 2023)
This work attempts to study the numerical solution of nonlinear delayed Immunized Susceptible Latent Infected and Recovered (MSLIR) epidemic model of HBV disease. Reproduc-tion number, equilibria and stability are discussed. Three different numerical techniques, Euler, RK-4 and the non-standard finite difference (NSFD) techniques are used for the numerical solution of the model. The proposed technique is independent of the size of the time step, while forward Euler and RK-4 depend on the size of a time step and retains all essential characteristics of the con-tinuous MSLIR epidemic model like positivity and stability of equilibrium, while well-known for-ward Euler and RK-4 cannot sustain these characteristics. Therefore, the proposed (NSFD) technique becomes a more efficient and reliable numerical technique than the forward Euler and RK-4 scheme. Numerical simulations are presented for the validation of the obtained results.(c) 2022 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Alexandria University. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/ licenses/by-nc-nd/4.0/).
Keywords: Hepatitis B virus (HBV); Time delay; Equilibrium points; Basic reproductive number; Global stability; Nonstandard finite difference method; Convergence analysis