Abstract
We present qualitative behavior of virus infection model with antibody immune response. The incidence rate of infection is given by saturation functional response. Two types of distributed delays are incorporated into the model to account for the time delay between the time when uninfected cells are contacted by the virus particle and the time when emission of infectious (matures) virus particles. Using the method of Lyapunov functional, we have established that the global stability of the steady states of the model is determined by two threshold numbers, the basic reproduction number R-0 and antibody immune response reproduction number R-1. We have proven that if R-0 <= 1, then the uninfected steady state is globally asymptotically stable (GAS), if R-1 <= 1 < R-0, then the infected steady state without antibody immune response is GAS, and if R-1 > 1, then the infected steady state with antibody immune response is GAS.