Mathematical modelling of the competition between tumors and immune system considering the role of the antibodies

A variety of immune system cells can recognize and destroy the autologous tumor cells. For the realization of the cytotoxic function of the effector cells, their close contact with the surface of the target cells is necessary. Such close contact can be realized not only through direct cell-cell recognition mechanism but also through some adaptor molecules (antibodies) binding with the effector cells and with the target cells. In the presented paper, this mechanism of the so-called humoral immunity is considered and described in a model of cellular tumor dynamics in competition with the immune system. The model is developed with statistical methods analogous to those of the kinetic theory. The model is expressed in terms of a system of integrodifferential equations. The role of the antibodies is taken into account. A numerical scheme for treating the system is proposed. The results of the computational simulations are presented and compared with some theoretical and experimental data.