某類三維癌症模型之整體穩定性分析

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姓名

黃亞妮(Puji Andayani) 查詢紙本館藏

畢業系所

數學系

論文名稱

某類三維癌症模型之整體穩定性分析
(Global Stability Analysis for Some Three-Dimensional Cancer Models)

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摘要(中)

此篇論文主要研究某類三維癌症模型的整體穩定性。此模型主要是描述宿主細胞、免疫效應細胞及腫瘤細胞之間的影響。根據所考慮的參數，此模型最多有
七個孤立的平衡點。我們首先給出保證各個平衡點存在的充分條件。同時我們證明當起始值位於第ㄧ卦限時模型解的有界性。接著我們利用常微分方程標準的方法及中心流形理論探討平衡點的線性穩定性。我們可以將所考慮的參數分為兩大類來探討平衡點的線性穩定性。此模型於其中一類參數考慮下並不存在正的平衡點，我們進一步嚴格證明此模型解的行為終將收斂至邊界的平衡點。同時我們提供一些數值結果驗證所得之理論成果。對於另ㄧ類參數，我們則提供了一些數值結果。從數值結果顯示此模型解在不同參數下，不僅俱有整體穩定性之特性同時亦呈現出解的混沌現象。

摘要(英)

In this thesis, we consider the global stability for some three dimensional cancer model which describes interaction between the host cells, the effector immune cells, and the tumor cells. According to the parameters on the models, there are at most seven isolated equilibria. We first provide some sufficient conditions that guarantee the existence of various kinds of positive equilibria for the system. Then we show that all solutions of the system are bounded when the initial data belong to the first quadrant. Next, we analyze the local stability of the equilibria by using the standard method of ODE and center manifold theory. The linearized stability result can be haracterized by two categories of the parameters. In one of the categories, there exists no positive equilibrium and we rigorously prove that all solutions trajectories converge to the boundary equilibria. We also perform some numerical simulations to support the main results. For another category, we provide some numerical results which demonstrate not only the global stability behavior but also the existence of chaotic phenomena.

關鍵字(中)

★ 宿主細胞
★ 免疫效應細胞
★ 腫瘤細胞
★ 中心流形理論
★ Dulac 標準
★ Poincaré-Bendixson 定理
★ omega-極限集

關鍵字(英)

★ host cells
★ effector-immune cells
★ tumor cells
★ center manifold theory
★ Dulac’s criterion
★ Poincar´e-Bendixson theorem
★ omega-limit set

論文目次

Contents
Chinese Abstract i
Abstract ii
Acknowledgements iii
Tables vi
Figures vii
1 Introduction 1
2 Equilibria and boundedness of solutions 3
2.1 Existence of equilibria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.2 Boundedness of solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
3 Local stability of the equilibria 7
3.1 Local stability for A0, A1 and A2 . . . . . . . . . . . . . . . . . . . . . . . 7
3.2 Local stability for A
3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
3.3 Local stability for A
4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
4 Stability analysis for non-hyperbolic equilibria 11
5 Global stability of the boundary equilibria 13
6 Numerical Result 20
6.1 Global stability phenomena . . . . . . . . . . . . . . . . . . . . . . . . . . 21
6.2 Chaotic phenomena . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
7 Conclusions 25
Reference 27

參考文獻

[1] L. G. de Pillis and A. Radunskaya, The dynamics of an optimally controlled tumor model: A case study, Mathematical and Computer Modelling, 37 (2003), 1221-1244.
[2] B.L. Gause, M. Sznol, W.C. Kopp, J. E. Janik, J.W, Smith II, JR. G. Steis, W.J. Urba, W. Sharfman, R.G. Fenton, S.P. Creekmore, J. Holmlund, K.C. Canlon, L.A. Vandermolen and D. L. Longo, Phase I study of subcutaneously
administered Interleukin-2 in combination with Interferon Alfa-2a in patients with advanced cancer, Journal of Clinical Oncology, Vol. 14, No. 8 (1996), 2234-2241.
[3] J. Guckenheimer and P. Holmes, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of vector Fields, Applied Mathematical Sciences 42, Springer-Verlag, 1983.
[4] S. B. Hsu, S. Ruan and T.H. Yang, Global dynamics of lotka-volterra food web models with omnivory, preprint, (2013).
[5] M. Itik and S.P. Banks, Chaos in a three dimensional cancer model, International Journal of Bifurcation and Chaos, Vol. 20, No. 1 (2010), 71-79.
[6] H.V. Jain, S.K. Clinton, A. Bhinder and A. Friedman, Mathematical modeling of prostate cancer progression in response to androgen ablation therapy, PNAS Biological Sciences, Vol. 108, No. 49 (2011), 19701-19706.
[7] Y. Kang and L. Wedekin, Dynamics of a intraguild predation model with generalist or specialist predator, J. Math. Biol., 67 (2013), 1227-1259.
[8] D. Kirschner and J. C. Panetta, Modeling immunotherapy of the tumor-immune interaction, J. Math. Biol., 37 (1998), 235-252.
[9] N. Kronik, Y. Kogan and V. Vainstein, Improving alloreactive CTL immunotherapy for malignant gliomas using a simulation model of their interactive dynamics, Journal of Cancer Immunology, Immunotherapy ,Vol. 57, No.3 (2008), 425-439.
[10] V. A. Kuznetsov and I. A. Makalkin, Nonlinear dynamics of immunogenic tumors: parameter estimation and global bifurcation analysis, Bull.Math. Biol. 56 (1994), 295-321.
[11] C. Latellier, F. Denis and L.A. Aguirre, What can be learned from a chaotic cancer Model. J.Theor.Biol., Vol. 322 (2013), 7-16.
[12] L. Perko, Differential Equations and Dynamical systems, Texts in Applied Mathematics 7, Springer-Verlag, 1990.
[13] J. P. Previte and K. A. Hoffman, Chaos in a predator-prey model with an omnivore, preprint, (2010).
[14] T. Roose, S.J. Chapman and P.K. Maini, Mathematical models of avascular tumor growth, SIAM Rev., Vol. 49, No. 2 (2007), 179-208.

指導教授

許正雄(Cheng Hsiung, Hsu)

審核日期

2014-7-15

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