Mathematical Study of In-host Dynamics of Hepatitis B Virus in Absence of Immunity System
Jannatun Nayeem *
Department of Arts and Sciences, Ahsanullah University of Science and Technology, Bangladesh.
Chandra N. Podder
Department of Mathematics, University of Dhaka, Bangladesh.
*Author to whom correspondence should be addressed.
Abstract
We develop a mathematical model to understand the dynamics of HBV-in host infection of individuals in vivo. The model incorporates the uninfected host cells, short lived infected cells, chronically infected cells, free virus particles, humoral immune response of HBV specific antibodies and cell mediated immune response of CTLs is analysed to gain its characteristic within human cell mechanism. At first we have analyzed the stability analysis of host cells and infected cells without the effect of immunity system and also discuss the graphical analysis with immunity system. Present study represents a mathematical model, which exhibit two equilibrium points namely, the virus free equilibrium (VFE) and virus present equilibrium (VPE). It is found that using Lyapunov function the virus free equilibrium (VFE) is globally asymptotically stable (GAS) when R0 < 1. And also the virus present equilibrium point (VPE) is locally asymptotically stable when R0 > 1.
Keywords: Hepatitis B virus in host (HBV-in host), basic reproduction number, equilibrium points, local and global stability, Laypunov function