Global analysis of the initial value problem for a system of O.D.E. modeling the immune system after vaccinations

A model of the human immune system after a series of vaccinations, proposed in [1], is studied, and a global qualitative study of the model in some special cases is proposed. It is shown that all solutions of the model have at most most one maximum at some point tm, next, for t > tm, t→ + ∞, monotonically tend to a physiological level, according to the behavior of antibody concentration observed in reality.