前列腺癌是一種影響老年男性的惡性腫瘤.這種惡性腫瘤集中在前列腺細(xì)胞中,但有時(shí)會(huì)擴(kuò)散到周圍組織和身體其他部位.這種類型的癌癥通常發(fā)展緩慢,可以完全消除或診斷后成功治療.但不幸的是,它可能是致命的.許多數(shù)學(xué)研究都集中在生物數(shù)學(xué)和醫(yī)學(xué)上,以期對(duì)治療策略有一個(gè)新的認(rèn)識(shí).因此,本論文的目的是研究前列腺癌的演變和發(fā)展,揭示不同治療方式的療效.在第一章中,介紹了前列腺癌的生物學(xué)背景、目前的治療方法、與我們工作相關(guān)的前列腺癌模型的重要進(jìn)展.本章也介紹了一些相關(guān)數(shù)學(xué)術(shù)語(yǔ)和定理.同時(shí),簡(jiǎn)要說(shuō)明了本論文的主要貢獻(xiàn).第二章研究了連續(xù)雄激素抑制治療下前列腺癌的隨機(jī)模型,研究了噪聲和劑量對(duì)治療策略的影響.在隨機(jī)系統(tǒng)中,噪聲對(duì)腫瘤細(xì)胞的持續(xù)和消亡起重要作用,得到了系統(tǒng)平均滅絕和持續(xù)的閾值條件.得到平穩(wěn)分布存在的充分條件.進(jìn)一步,利用數(shù)值模擬的方法對(duì)最優(yōu)處理策略進(jìn)行估計(jì),最后我們考慮周期性治療對(duì)該模型的影響并得到此種情況下周期解存在的充分條件.該模型說(shuō)明由于噪音干擾的作用,一種與腫瘤細(xì)胞復(fù)制相關(guān)的藥物有利于用CAS治療策略.另外,分析結(jié)果表明如果醫(yī)生找不到治療癌癥的方法,他們可以嘗試去研制一種能夠降低耐藥細(xì)胞活性的藥... 

【文章頁(yè)數(shù)】：121 頁(yè)

【學(xué)位級(jí)別】：博士

【文章目錄】：
摘要
Abstract
Chapter 1 Introduction
    1.1 Background of prostate cancer and treatment
        1.1.1 Hormone therapy
        1.1.2 Immunotherapy
        1.1.3 Further treatments
    1.2 Literature review of mathematical models
    1.3 Contributions
    1.4 Background of stochastic noise and bifurcation theory
        1.4.1 Stochastic differential equations
        1.4.2 Bifurcation theory
Chapter 2 Stochastic model of CAS therapy
    2.1 Model formulation
    2.2 Mathematical analysis
        2.2.1 Existence and uniqueness of solution
        2.2.2 Persistence in mean and extinction
        2.2.3 Stationary distribution and ergodicity for system
    2.3 Approximation of optimal treatment
    2.4 Extension to periodic treatment
        2.4.1 Qualitative results
        2.4.2 Existence of periodic solutions
        2.4.3 Numerical simulations
    2.5 Conclusions
Chapter 3 Bifurcation in immunotherapy model
    3.1 Mathematical model
    3.2 Dynamics of model without immunotherapy
        3.2.1 Equilibrium points and their stability
        3.2.2 Bifurcation analysis
    3.3 Bifurcation of model with immunotherapy
        3.3.1 The effect of dendritic cells vaccines on tumor cells
        3.3.2 Periodic behavior of tumor cells
    3.4 Conclusions
Chapter 4 Discussions
References
Academic papers completed and published during the Ph.D.
Acknowledgement



本文編號(hào)：3686865