A MATHEMATICAL MODEL SIMULATING THE EFFECT OF VACCINE INDUCED RESPONSES ON HIV-1 INFECTION

We analyze the mathematical model of the dynamics of HIV-1 infection in an organism reported in [9]. The model consists of a set of second type delay Volterra Integral Equations and takes into account the induction upon vaccination of a humoral and/or cellular immune response; the existence of a distributed delay for intracellular life cycle of the virus and a maximal time period for which an infected cell is allowed to become productive. We perform the analysis of the qualitative behavior of the solution by proving its positivity, boundedness and by providing a threshold parameter whose value permits to predict whether the infection will spread in the organism or not. Some numerical examples are added even if most of numerical analysis of the model is carried out in [9].