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.
Highlights
Hepatitis B is an infectious disease that is a global concern and a major cause of death worldwide [1].This disease is disseminated by means of the hepatitis B virus (HBV) through various forms of transmission.a susceptible person may be infected through blood transfusion, exchange of saliva, use of contaminated razors and needles, sexual contact with an infected person, and even through acupuncture and piercing instruments, among other forms of transmission [2]
We investigated numerically a susceptible-infected-recovered hepatitis B epidemic reaction-diffusion model in three spatial dimensions
To study the dynamics of this system, we proposed a structure-preserving nonstandard finite-difference splitting numerical method
Summary
Hepatitis B is an infectious disease that is a global concern and a major cause of death worldwide [1]. The present work is motivated by the following susceptible-infected-recovered model for hepatitis B with saturated incidence rates: dX1 (t) = λ − αX1 (t) X2 (t) − (μ0 + ν) X1 (t), In this model, X1 , X2 , X3 : R+ ∪ {0} → R are sufficiently smooth functions that represent the total of susceptible, infected and recovered individuals, respectively. X1 , X2 , X3 : R+ ∪ {0} → R are sufficiently smooth functions that represent the total of susceptible, infected and recovered individuals, respectively This model was proposed recently in [29] as a mathematical model of transmission of hepatitis B, and its inhibition effects are the most notable physical features. The simulations will shed light on the validity of the theoretical results obtained in this work
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