發(fā)布時(shí)間：2021-10-17 09:31

　　西尼羅河病毒（WNv）是一種發(fā)現(xiàn)于溫帶和熱帶的病毒.這類病毒持續(xù)在世界各地傳播且對(duì)于野生生物和公眾健康依然是一個(gè)重大威脅.我們知道,由于引發(fā)WNv的不是細(xì)菌而是一種病毒性病原體,因此醫(yī)學(xué)上目前還沒有有效的疫苗和抗生素.除了驅(qū)蚊劑等一些預(yù)防措施以外對(duì)于WNv我們還沒有明確有效的治療措施.故從數(shù)學(xué)上來說理解WNv的傳播動(dòng)力學(xué)至關(guān)重要.早期多數(shù)的模型只考慮了和空間無關(guān)的參數(shù),然而空間擴(kuò)散是影響傳染病持續(xù)和消退的一個(gè)重要因素,因此本篇博士論文主要使用數(shù)學(xué)模型和偏微分方程理論知識(shí)來研究WNv的時(shí)空傳播特征.首先,我們?cè)诘谝徽陆榻B了西尼羅河病毒傳播的一些背景知識(shí)和已有的研究進(jìn)展.第二章研究了西尼羅河病毒傳播的擴(kuò)張進(jìn)程.我們考慮了耦合系統(tǒng)的自由邊界問題,其中用一個(gè)偏微分方程來描述鳥的擴(kuò)散,而用一個(gè)常微分方程來刻畫蚊子的活動(dòng).通過拉直自由邊界,應(yīng)用壓縮映象原理證明了解的全局存在唯一性,并且提出了比較原理.我們定義了與空間無關(guān)模型的基本再生數(shù),并且通過考慮相應(yīng)的特征值問題引入了對(duì)應(yīng)的具Dirichlet邊界條件問題的閾值.最后考慮空間情形下,引入風(fēng)險(xiǎn)指標(biāo)并且討論其性質(zhì).利用該風(fēng)險(xiǎn)指標(biāo),給出了西尼羅河病毒... 

【文章來源】：揚(yáng)州大學(xué)江蘇省

【文章頁數(shù)】：156 頁

【學(xué)位級(jí)別】：博士

【文章目錄】：
中文摘要
Abstract
Chapter 1 Introduction
    1.1 West Nile virus and its transmission
    1.2 Mathematical models of WNv
    1.3 Simplified models of WNv
    1.4 Motivations and contributions
Chapter 2 Spreading and vanishing in a WNv model with expandingfronts
    2.1 The model with expanding fronts
    2.2 Existence and uniqueness of the solution
    2.3 The risk index of WNv
    2.4 The vanishing of WNv
    2.5 The spreading of WNv
    2.6 Numerical simulations and discussions
Chapter 3 Coexistence of a cross-diffusive WNv model in a hetero-geneous environment
    3.1 The WNv model with cross-diffusion
    3.2 Basic reproduction numbers
    3.3 Existence of coexistence
    3.4 Non-existence of coexistence
    3.5 Iteration and true solution
    3.6 Numerical simulations and discussions
Chapter 4 Asymptotic periodicity in a diffusive WNv model in aheterogeneous environment
    4.1 Periodic phenomena and the model
    4.2 Basic reproduction numbers
    4.3 Existence and non-existence of periodic solution
    4.4 The maximal and minimal periodic solutions
    4.5 Attractivity of periodic solutions
    4.6 Numerical simulations and discussions
Chapter 5 The spatial-temporal risk index and transmission dynam-ics for a time-periodic diffusive WNv model
    5.1 Periodic surrounding and free boundary
    5.2 Preliminaries
    5.3 The spatial-temporal risk index
    5.4 The T-periodic boundary value problem in half line
    5.5 Spreading and vanishing
    5.6 Numerical simulations and discussions
Chapter 6 Conclusions and future research
Bibliography
Publications
Acknowledgements



本文編號(hào)：3441534