Stability Analysis and Simulation of a Fractional-order HBV Infection Model Based on Saturation Incidence

Abstract

Fractional order model has the memory, while the characteristic of the immune response contains the memory. In this paper, we set up a fractional-order HBV immune model based on saturation incidence for the first time. We derive the basic reproductive number R0, the cytotoxic T lymphocytes immune response reproductive number R1. There are three equilibrium points of our model, the local stability of each equilibrium point was given with corresponding hypothesis about R0 or R1. Finally we also give some numerical simulation, the simulation shows the individual difference in clinical may be reflected by fractional-order model.