Hopf-Andronov-Poincare bifurcation in cancer chemotherapy
The principles of mathematical modeling and analyses are applied to chemotherapy of human cancers. Clinical complications associated with cancer chemotherapy are analyzed using a model consisting of a system of generalized nonlinear deterministic ordinary differential equations. The model incorporates patho-physiological interactions between cancer cells, noncancerous cells, and anticancer drug molecules in an anatomic space within a cancer patient. The anticancer drug is assumed to be specifically cytotoxic selectively to cancer cells. The bio-physiological interactions between cancer cells, non-cancer cells and anticancer drug molecules are depicted by real-valued positive stoichiometric rate constants, Sufficient conditions are provided such that the model equations are well-posed in the sense of Hadamard, positively invariant and the solutions are ultimately bounded. Explicit mathematical criteria are provided under which Hopf-Andronov-Poincare bifurcation can occur during chronic chemotherapy. Computer simulations are presented illustrating some of the therapeutic outcomes.
Anim, Kofi Asare, "Hopf-Andronov-Poincare bifurcation in cancer chemotherapy" (2015). ETD Collection for Fayetteville State University. AAI1581857.