Analysis of Some Mathematical Models for the Spatial Transmi
发布时间：2021-10-17 09:31
西尼罗河病毒（WNv）是一种发现于温带和热带的病毒.这类病毒持续在世界各地传播且对于野生生物和公众健康依然是一个重大威胁.我们知道,由于引发WNv的不是细菌而是一种病毒性病原体,因此医学上目前还没有有效的疫苗和抗生素.除了驱蚊剂等一些预防措施以外对于WNv我们还没有明确有效的治疗措施.故从数学上来说理解WNv的传播动力学至关重要.早期多数的模型只考虑了和空间无关的参数,然而空间扩散是影响传染病持续和消退的一个重要因素,因此本篇博士论文主要使用数学模型和偏微分方程理论知识来研究WNv的时空传播特征.首先,我们在第一章介绍了西尼罗河病毒传播的一些背景知识和已有的研究进展.第二章研究了西尼罗河病毒传播的扩张进程.我们考虑了耦合系统的自由边界问题,其中用一个偏微分方程来描述鸟的扩散,而用一个常微分方程来刻画蚊子的活动.通过拉直自由边界,应用压缩映象原理证明了解的全局存在唯一性,并且提出了比较原理.我们定义了与空间无关模型的基本再生数,并且通过考虑相应的特征值问题引入了对应的具Dirichlet边界条件问题的阈值.最后考虑空间情形下,引入风险指标并且讨论其性质.利用该风险指标,给出了西尼罗河病毒...
【文章来源】：扬州大学江苏省
【文章页数】：156 页
【学位级别】：博士
【文章目录】：
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
本文编号：3441534
【文章来源】：扬州大学江苏省
【文章页数】：156 页
【学位级别】：博士
【文章目录】：
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
本文编号：3441534
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