In recent years, the study of immune response behaviour through mathematical and computational models has been the focus of considerable efforts. We propose a mesoscopic model to combine the most useful features of the microscopic and macroscopic approaches, which have been the alternatives to date. Cellular automata and Monte Carlo simulation are used to describe the humoral and T-cell mediated immune response, where the nature of the response induced depends on the polarization of T_H1 and T_H2 cells. Memory immunity is introduced to our model, so that we can simulate primary and secondary immune response. The high affinity between memory B-cells and antibodies contributes to a quick and intense response to repeated infection. The experiments on P_affB--AB and P_affMB--AB, which control antibody production, explore the different roles of B-cell and memory B-cell in immune response stages. The duration of immunological memory is also studied.