Hopf-Andronov-Poincare bifurcation in cancer chemotherapy

Kofi Asare Anim, Fayetteville State University


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.

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Recommended Citation

Anim, Kofi Asare, "Hopf-Andronov-Poincare bifurcation in cancer chemotherapy" (2015). ETD Collection for Fayetteville State University. AAI1581857.