Abstract
We consider a mathematical model describing Intermittent Androgen Suppression therapy (IAS therapy) of prostate cancer. The system has a hybrid structure, i.e., the system consists of two different systems by the medium of an unknown binary function denoting the treatment state. In this paper, we shall prove that the hybrid system has a unique solution with the property that the binary function keeps on changing its value. In the clinical point of view, the result asserts that one can plan the IAS therapy for each prostate cancer patient, provided that the tumor satisfies a certain condition.
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Acknowledgments
The second author was partially supported by Grant-in-Aid for Young Scientists (B), No. 24740097, and by Strategic Young Researcher Overseas Visits Program for Accelerating Brain Circulation (JSPS). The authors would like to express their gratitude to Professor Izumi Takagi of Tohoku University who gave them many useful comments.
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Hiruko, K., Okabe, S. (2016). Dynamical Aspects of a Hybrid System Describing Intermittent Androgen Suppression Therapy of Prostate Cancer. In: Gazzola, F., Ishige, K., Nitsch, C., Salani, P. (eds) Geometric Properties for Parabolic and Elliptic PDE's. GPPEPDEs 2015. Springer Proceedings in Mathematics & Statistics, vol 176. Springer, Cham. https://doi.org/10.1007/978-3-319-41538-3_12
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