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    政大機構典藏 > 理學院 > 應用數學系 > 期刊論文 >  Item 140.119/62300
    Please use this identifier to cite or link to this item: http://nccur.lib.nccu.edu.tw/handle/140.119/62300


    Title: Optimal Policies of Non-Cross-Resistant Chemotherapy on Goldie and Coldman's Cancer Model
    Authors: 陳政輝
    Chen, Jeng-Huei
    郭雅慧
    Kuo, Ya-Hui
    陸行
    Luh, Hsing Paul
    Contributors: 應數系
    Keywords: Goldie and Coldman’s model;Drug resistance;Optimal cancer treatment
    Date: 2013.10
    Issue Date: 2013-12-09 13:37:00 (UTC+8)
    Abstract: Mathematical models can be used to study the chemotherapy on tumor cells. Especially, in 1979, Goldie and Coldman proposed the first mathematical model to relate the drug sensitivity of tumors to their mutation rates. Many scientists have since referred to this pioneering work because of its simplicity and elegance. Its original idea has also been extended and further investigated in massive follow-up studies of cancer modeling and optimal treatment. Goldie and Coldman, together with Guaduskas, later used their model to explain why an alternating non-cross-resistant chemotherapy is optimal with a simulation approach. Subsequently in 1983, Goldie and Coldman proposed an extended stochastic based model and provided a rigorous mathematical proof to their earlier simulation work when the extended model is approximated by its quasi-approximation. However, Goldie and Coldman’s analytic study of optimal treatments majorly focused on a process with symmetrical parameter settings, and presented few theoretical results for asymmetrical settings. In this paper, we recast and restate Goldie, Coldman, and Guaduskas’ model as a multi-stage optimization problem. Under an asymmetrical assumption, the conditions under which a treatment policy can be optimal are derived. The proposed framework enables us to consider some optimal policies on the model analytically. In addition, Goldie, Coldman and Guaduskas’ work with symmetrical settings can be treated as a special case of our framework. Based on the derived conditions, this study provides an alternative proof to Goldie and Coldman’s work. In addition to the theoretical derivation, numerical results are included to justify the correctness of our work.
    Relation: Mathematical Biosciences, 245(2), 282-298
    Data Type: article
    DOI 連結: http://dx.doi.org/10.1016/j.mbs.2013.07.020
    DOI: 10.1016/j.mbs.2013.07.020
    Appears in Collections:[應用數學系] 期刊論文

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