  We consider the model of interaction between the immune system and tumor
cells including a memory function that reflect the influence of the past
states, to simulate the time needed by the latter to develop a chemical and
cell mediated response to the presence of the tumor. The memory function is
called delay kernel. The results are compared with those from other papers,
concluding that the memory function introduces new instabilities in the system
leading to an uncontrolable growth of the tumor. If the coefficient of the
memory function is used as a bifurcation parameter, it is found that Hopf
bifurcation occurs for kernel. The direction and stability of the bifurcating
periodic solutions are determined. Some numerical simulations for justifying
the theoretical analysis are also given.
