Predicting the potential impact of a cytotoxic T-lymphocyte HIV vaccine: How often should you vaccinate and how strong should the vaccine be?

To stimulate the immune system’s natural defenses, a post-infection HIV vaccination program to regularly boost cytotoxic T-lymphocytes has been proposed. We develop a mathematical model to describe such a vaccination program, where the strength of the vaccine and the vaccination intervals are constant. We apply the theory of impulsive differential equations to show that the model has an orbitally asymptotically stable periodic orbit, with the property of asymptotic phase. We show that, on this orbit, the vaccination frequency can be chosen so that the average number of infected CD4+ T cells can be made arbitrarily low. We illustrate the results with numerical simulations and show that the model is robust with respect to both the parameter choices and the formulation of the model as a system of impulsive differential equations.