Dynamics of a fractional order HBV infection model with capsids and CTL immune response

Abstract

In this article, a fractional order model for hepatitis B virus (HBV) infection with capsids and immune response presented by cytotoxic T lymphocyte (CTL) cells is proposed and investigated. The infection transmission is modeled by Hattaf-Yousfi functional response and the fractional derivative is in the Caputo sense. First, the well-posedness of the proposed model is proved in terms of existence, uniqueness, non-negativity and boundness of solutions. The global asymptotic stability of steady states is established by using suitable Lyapunov functionals and applying LaSalle’s invariance principle. Numerical simulations are performed to illustrate the analytical results.