Realization of features of immune response by dynamical system models and a possible mechanism of memory of antigen invasion

Among features of real immune responses which occur when antigens invade a body,there are two remarkable features. One is that the amount of antibodies produced in the secondary invasion by the same antigens is more than 10 times larger than that in the primary invasion. The other is that more effective antibodies which can neutralize the antigens more quickly are produced by somatic hypermutation during the immune response. This phenomenon is named as 'affinity maturation'. In this paper, we try to reproduce these features by dynamical system models and present possible factors to realize them. Further, we present a model in which the memory of the invasion by antigens is realized without immune memory cells.