Abstract:

In this paper, we study the stability of fractional-order HBV (Hepatitis B Virus) infection model with immune delay and nonlinear incidence. Initially, the existence, uniqueness, positivity and boundedness of the model solutions are discussed. In addition, with the stability theory of functional differential equation, combining some new lemmas about Caputo fractional derivatives and some theories about fractional dynamic system, we discuss the in?uence of time delay on the stability of equilibrium point by analyzing the distribution of the characteristic equation roots on the equilibrium point. The results show that time delay does not a?ect the stability of disease-free equilibrium, while induces the stability of endemic equilibrium and produces periodic solutions with small amplitude nearby. Meanwhile, global asymptotic stability of the disease-free equilibrium is investigated by constructing a suitable Lyapunov function. Finally, using the fractional order delay stability principle, the corresponding linear controller is designed to effectively control the fractional order HBV infection model.

Key words: Time delay, Fractional order, HBV, Stability