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Open AccessArticle

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

1
Departamento de Matemáticas y Física, Universidad Autónoma de Aguascalientes, Aguascalientes 20131, Mexico
2
Department of Mathematics and Statistics, University of the Lahore, Lahore 54590, Pakistan
3
Faculty of Engineering, University of Central Punjab, Lahore 54590, Pakistan
*
Author to whom correspondence should be addressed.
Mathematics 2019, 7(12), 1157; https://doi.org/10.3390/math7121157
Received: 11 October 2019 / Revised: 1 November 2019 / Accepted: 3 November 2019 / Published: 1 December 2019
(This article belongs to the Special Issue Computational Mathematics and Neural Systems)
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. View Full-Text
Keywords: splitting methods; hepatitis B epidemic dynamics; stability and bifurcation analyses; nonstandard finite-difference method splitting methods; hepatitis B epidemic dynamics; stability and bifurcation analyses; nonstandard finite-difference method
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Macías-Díaz, J.E.; Ahmed, N.; Rafiq, M. Analysis and Nonstandard Numerical Design of a Discrete Three-Dimensional Hepatitis B Epidemic Model. Mathematics 2019, 7, 1157.

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