Analysis and Nonstandard Numerical Design of a Discrete Three-Dimensional Hepatitis B Epidemic Model

Jorge E. Macías-Díaz, Nauman Ahmed and Muhammad Rafiq
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Jorge E. Macías-Díaz: Departamento de Matemáticas y Física, Universidad Autónoma de Aguascalientes, Aguascalientes 20131, Mexico
Nauman Ahmed: Department of Mathematics and Statistics, University of the Lahore, Lahore 54590, Pakistan
Muhammad Rafiq: Faculty of Engineering, University of Central Punjab, Lahore 54590, Pakistan

Mathematics, 2019, vol. 7, issue 12, 1-16

Abstract: In this work, we numerically investigate a three-dimensional nonlinear reaction-diffusion susceptible-infected-recovered hepatitis B epidemic model. To that end, the stability and bifurcation analyses of the mathematical model are rigorously discussed using the Routh–Hurwitz condition. Numerically, an efficient structure-preserving nonstandard finite-difference time-splitting method is proposed to approximate the solutions of the hepatitis B model. The dynamical consistency of the splitting method is verified mathematically and graphically. Moreover, we perform a mathematical study of the stability of the proposed scheme. The properties of consistency, stability and convergence of our technique are thoroughly analyzed in this work. Some comparisons are provided against existing standard techniques in order to validate the efficacy of our scheme. Our computational results show a superior performance of the present approach when compared against existing methods available in the literature.

Keywords: splitting methods; hepatitis B epidemic dynamics; stability and bifurcation analyses; nonstandard finite-difference method (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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