Stability of a Delayed Hepatitis B Virus Infection Model: Effect of Specific Functional Response and Absorption

This work proposes and investigates a delayed cell population model of hepatitis B virus (HBV) infection. We use the Hattaf-Yousfi incidence function to describe viral infection. The model takes into account a specific functional response and the usually neglected absorption effect. Moreover, we introduce a time delay to account for the transformation processes necessary for actual HBV production. We naturally find a threshold parameter, namely, the basic reproduction number which ultimately determines the stability of the equilibria of the model obtained under other conditions. We determine the equilibria of our model known as uninfected equilibrium and infected equilibrium, and show that the model is well-posed, mathematically and biologically. By constructing appropriate Lyapunov functionals and using LaSalle’s invariance principle, we show that, if the uninfected equilibrium is globally asymptotically stable. Furthermore, we prove that the uninfected equilibrium is locally asymptotically stable if