某類傳染病模型微分方程行波解之研究

以作者查詢圖書館館藏

、以作者查詢臺灣博碩士

、以作者查詢全國書目

、勘誤回報

、線上人數：132

、訪客IP：3.145.173.112

姓名

郭權緻(Chuan-chih Kuo) 查詢紙本館藏

畢業系所

數學系

論文名稱

某類傳染病模型微分方程行波解之研究
(Traveling Wave Solutions for Some EpidemicModels)

相關論文

★ 在只有部份疾病訊息狀況下,有關二元診斷篩檢法之二個概似比特徵之概似推論方法	★ 混合噪聲的即時圖像去噪在螢光顯微鏡圖像和古畫中的應用
★ 遲滯型細胞神經網路之行進波	★ 遲滯型細胞神經網絡行進波之結構
★ 網格型微分方程的行進波的數值解	★ 某類網格型微分方程行波解的存在性，唯一性及穩定性
★ 某類週期性網格型微分方程行波解之研究	★ 網格型動態系統行波解之研究
★ 矩陣值勢能上的sofic測度	★ 在Sofic Shift上的多重碎型分析
★ 某類三維癌症模型之整體穩定性分析	★ 三種競爭合作系統之行波解的存在性
★ 離散型Lotka-Volterra競爭系統之行波解的穩定性	★ On the Existence of the Stem Entropy on Markov-Cayley tree

檔案

[Endnote RIS 格式]

[Bibtex 格式]

[相關文章]

[文章引用]

[完整記錄]

[館藏目錄]

[檢視]

[下載]

本電子論文使用權限為同意立即開放。
已達開放權限電子全文僅授權使用者為學術研究之目的，進行個人非營利性質之檢索、閱讀、列印。
請遵守中華民國著作權法之相關規定，切勿任意重製、散佈、改作、轉貼、播送，以免觸法。

摘要(中)

在本篇論文中，我們主要研究某類傳染病模型的微分方程，其行波解的存
在且該行波解為monotonic。利用monotone iteration這個方法，結合我們所
建構的上解和下解，證明當存在最小的波速c* ，而且當波速高於最小波速
c* 時，行波解是存在的。

摘要(英)

The purpose of this thesis is to investigate the existence of monotonic traveling
wave solutions for some epidemic models. Using the monotone iteration method,
combining with a pair of upper solution and lower solution, we show that there
exist a minimal wave speed c* such that if the wave speed is greater than c* ,
then there exist monotone traveling wave solutions.

關鍵字(中)

★ monotone iterations
★ 上解
★ 下解
★ 行進波
★ 傳染病模型

關鍵字(英)

★ upper and lower
★ traveling wave
★ epidemic model

論文目次

中文摘要........................................................................................................i
英文摘要.......................................................................................................ii
Contents.......................................................................................................iii
Abstract.........................................................................................................1
1. Introduction...............................................................................................2
2. Local Analysis and Minimal Wave Speed............................................5
3. Solution Operator and Its Properties.........................................................8
4. Construction of Upper and Lower Solutions...........................................10
5. Proof of the Main Theorem.....................................................................14
References...................................................................................................17

參考文獻

[1] D. G. Aronson and H. F. Weinberger, Nonlinear diffusion in population
genetics, combustion, and nerve pulse propagtion, in partial differential
equations and related topics, Lecture Notes in Mathematics, 446,
Spring-Verlag, 1975, 5-49.
[2] V. Capasso, Mathematical structures of epidemic systems, Lecture
Notes in Biomath. 97, Springer-Verlag, Heidelberg,1993.
[3] V. Capasso and K. Kunisch, A reaction-diffusion system arising in
modelling man-environment diseases, Quart. Appl. Math. 46 (1988),
431-450
[4] E. A. Coddington and N. Levinson, Theory of Ordinary Differential
Equations, McGraw-Hill, New York, 1995.
[5] V. Capasso and S. L. Paveri-Fontana, A mathmatical model for the
1973 cholera epidemic in the European Mediterranean region, Revue
d’Epidemiol. etde Sant’e Publique 27 (1979), 121-132
[6] V. Capsso and R. E. Wilson, Analysis of reaction-diffusion system
modeling man-environment-man epidemics,SIAM. J. Appl. Math. 57
(1997), 327-346.
[7] O. Diekmann, Thresholds and traveing waves for the geographical
spread of infection, J. Math. Biology, 6 (1978), 109-130.
[8] P. C. Fife, Mathematical Aspects of Reacting and Diffusing System,
Lecture Notes in Biomath. 28, Springer-Verlag, Berlin and New York,
1979.
[9] S. A. Gourley, Travelling front solutions of a nonlinear diffusion equations,
J. Math. Biology, 41 (2000), 272-284.
[10] K. P. Hadeler, Nonlinear propagation in reaction transport systems,
in differential equations with applications to biology, Fields Inst. Commun.,
21, AMS, Providednce, RI, 1999, 251-257.
[11] K. P. Hadeler and F. Rothe, Travelling fronts in nonlinear diffusion
equations, J. Math. Biology, 2 (1975), 251-263.
[12] J. D. Murray, Mathematical Biology, Springer-verlag, New York, 1989.
[13] S. Ma, Travelling wavefronts for delayed reaction-diffusion systems via
a fixed point theorem, J. Diff. Eqns., 171 (2001), 251-263.
[14] K. W. Schaaf, Asymptotic behavior and traveling waves aolutions for
parabolic functional differential equations, Trans. Amer. Math. Soc.,
302 (1987), 587-615.
[15] H. L. Smith and X.-Q. Zhao, Global asymptotic stabiliy of traveling
waves in delayed reaction-diffusion eqautions, SIAM J. Math. Anal.,31
(2000), 514-534.
[16] A. I. Vopert, Vitaly A. Volpert and Vladimir A. Volpert, Traveling
Waves Solutions of Parabolic Systems, Translation of Mathematical
Monographs, 140, Amer. Math. Soc., 1994.
[17] J. Wu, Theory and Applications of Parical Functional Differential
Equations, Springer-Verlag, New York, 1996.
[18] J. Wu and X. Zou, Travling wave fronts of reaction-diffusion systems
with delay, J. Dynamics and Differential Equations, 13 (2001), 651-687.
[19] X. Q Zhao and Z. T. Jing, Global asymptotic behavior in some cooperative
systems of functional differential equations, Canadian Applied
Mathematics Quarterly, 4 (1996), 421-444.
[20] X. Q. Zhao and W. Wang, Fisher waves in an epidemic model, Disc.
Conti. Dyn. Sys. Ser. B4 (2004), 1117-1128.

指導教授

許正雄(Cheng-hsiung Hsu)

審核日期

2012-7-12

推文