Mathematical and Computer Modelling
By adapting a pre-existing model to include the effects of vascularization within a tumor or multicell spheroid, a predator-prey system describing the cell populations of a solid tumor and reactive lymphocytes is formulated. The paper serves as a review of the minimal deterministic approach to tumor-host immune system interactions while examining, in a qualitative manner, the modifications to the dynamics induced by a simple representation of the vascularized tumor. In addition, the possibility of limit-cycle behavior is studied by regarding each of six parameters present in the model as a bifurcation parameter. Thus, in principle, well-defined and periodic oscillations in both lymphocyte and tumor cell populations may occur under appropriate circumstances; whether or not such oscillations are sustainable by the host, and their stability, amplitude and period depend on aquisition of more quantitative information concerning the relevant parameter ranges.
Original Publication Citation
Adam, J. A. (1996). Effects of vascularization on lymphocyte/tumor cell dynamics: Qualitative features. Mathematical and Computer Modelling, 23(6), 1-10. doi:10.1016/0895-7177(96)00016-7
Adam, J. A., "Effects of Vascularization on Lymphocyte/Tumor Cell Dynamics: Qualitative Features" (1996). Mathematics & Statistics Faculty Publications. 92.