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研究生： 成自然
CHENG, ZIRAN
論文名稱： 探討一個抗生素及細菌突變之動力數學模型及其數學分析
Dynamics of drug on-drug off model with mutations
指導教授： 許世壁
HSU, SZE-BI
蔡志強
TSAI, JE-CHIANG
口試委員: 王埄彬
WANG, FENG-BIN
王信華
WANG, SHIN-HWA
學位類別： 碩士
Master
系所名稱： 理學院 - 數學系
Department of Mathematics
論文出版年： 2019
畢業學年度： 108
語文別： 英文
論文頁數： 27
中文關鍵詞： 藥物注射系統 、細菌突變 、生物培養裝置 、全局穩定
外文關鍵詞： drug on-drug off model, mutation, morbidostat, global stability
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    • Morbidostat 是一個通過不斷提高抗生素濃度來研究細菌演化進程的細菌培養裝置。在本文中，我們首先設置了一個合理的假設條件，並在該假設條件下證明了藥物注射系統的解的有界性。 隨後，我們分別分析了在三種不同突變情況下系統的局部和全域穩定性。最後，我們總結了當閾值參數U發生改變時，包括原生細菌和突變體在內的所有物種的生存狀況。

    The morbidostat is a bacteria culture device that progressively increases antibiotic drug concentration and maintains a constant challenge for study of evolutionary pathway \cite{5}. In this work, we first change the hypothesis of \cite(5) in a more reasonable way, and prove the boundedness of the solutions in drug on-drug off system. Then we analyze the local stability and global stability of the system with no mutation, only forward mutation and forward-backward mutation respectively. We conclude the survival condition of all species including the wide type and the mutants when the threshold parameter U varies.

    1.Introduction and models . . . . . . . . . . .1 1.1.Introduction. .. . . . . . . . . . . . . . .1 1.2.Description of the models. . . . . . . . . . 2 2.Preliminary . . . . . . . . . . .4 3.Dynamics of drug on-drug o model with no mutations . . . . . . 4 3.1.The behavior of solutions of the system (3.1) . . . . . . .4 3.2.The results of the asymptotic behavior of the solutions of model with no mutations . . . . . . . . . . . . . . . . . . 7 4.Dynamics of drug on-drug o model with only forward mutations. . . . . . . . . . .11 4.1.The behavior of the solutions of the system (4.1) . . . . . 11 4.2.The results of the asymptotic behavior of the solutions of model with only forward mutations . . . . . . .. . . . . .21 5.Dynamics of drug on-drug o model with forward-backward mutations . . . . . . . . . . .23 6.Numerical simulations. . . . . . . . . . .25 7.References. . . . . . . . . . .27

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    (5)Z. Chen, S.B. Hsu and Y.T. Yang, {\em The continuous Morbidostat : a chemostat controlled drug application to select for drug resistance mutants}, Communications on Pure \& Applied Analysis, 2020, 19 (1) : 203-220.
    (6)Z. Chen, S.B. Hsu and Y.T. Yang, {\em The Morbidostat: A Bio-reactor That Promotes Selection for Drug Resistance in Bacteria},
     SIAM Journal on Applied Mathematics 77(2017):470-499.
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