Qualitative analysis of an integro-differential equation model of periodic chemotherapy. (English) Zbl 1386.45010
Summary: An existing model of tumor growth that accounts for cell cycle arrest and cell death induced by chemotherapy is extended to simulate the response to treatment of a tumor growing in vivo. The tumor is assumed to undergo logistic growth in the absence of therapy, and treatment is administered periodically rather than continuously. Necessary and sufficient conditions for the global stability of the cancer-free equilibrium are derived and conditions under which the system evolves to periodic solutions are determined.
MSC:
| 45J05 | Integro-ordinary differential equations |
| 34K20 | Stability theory of functional-differential equations |
| 34K13 | Periodic solutions to functional-differential equations |
| 92C50 | Medical applications (general) |
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