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.
Bibliographical noteFunding Information:
The authors thank Profs Avner Friedman and Marty Golubitsky and Drs Rachel Leander and Yunjiao Wang for many helpful discussions. This research has been supported in part by the MBI and the NSF (grant DMS 0931642 ). This publication is based on work supported in part by Award No. KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST).
Copyright 2012 Elsevier B.V., All rights reserved.
- Nonautonomous logistic growth
- Periodic orbit
- Stability analysis