Abstract
In this paper, we propose a fractional reaction-diffusion model in order to better understand the mechanisms and dynamics of hepatitis B virus (HBV) infection in human body. The infection transmission is modeled by Hattaf–Yousfi functional response, and the fractional derivative is in the sense of Caputo. The global stability of the model equilibria is analyzed by means of Lyapunov functionals. Finally, numerical simulations are presented to support our analytical results.
Highlights
In the recent years, fractional calculus has attracted the attention of many researchers
It affects the lives of 257 million people and responsible for the deaths of 56000 people every year according to World Health Organization (WHO) estimates [7]. erefore, several mathematical models have been proposed and developed to describe the dynamics of hepatitis B virus (HBV) infection
We propose the following mathematical model formulated by fractional partial differential equations (FPDEs) to better describe the dynamics of HBV infection under the effects of diffusion and memory: Discrete Dynamics in Nature and Society zαt U σ − δU(x, t) − F(U(x, t), zαt I F(U(x, t), V(x, t))V(x, t)
Summary
Fractional calculus has attracted the attention of many researchers. Erefore, several mathematical models have been proposed and developed to describe the dynamics of HBV infection. Guo et al [10] studied a nonlinear system of partial differential equations (PDEs) for HBV infection with three time delays, general incidence rate, and spatial diffusion only in the viruses. Since fractional-order models possess property of memory, Bachraou et al [12] proposed a mathematical model governed by fractional differential equations (FDEs) to more explore the dynamic characteristics of the HBV infection. We propose the following mathematical model formulated by fractional partial differential equations (FPDEs) to better describe the dynamics of HBV infection under the effects of diffusion and memory: Discrete Dynamics in Nature and Society.
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