Dynamics of Delayed Systems with Applications to Ecoepidemiology

延迟系统动力学及其在生态流行病学中的应用

• 批准号: RGPIN-2014-04420
• 负责人: Chen, Yuming
• 金额: $ 1.31万
• 依托单位: Wilfrid Laurier University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2015
• 资助国家: 加拿大
• 起止时间: 2015-01-01 至 2016-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=587797
• 关键词: Dynamics; Delayed; Systems; Applications; Ecoepidemiology

Ecoepidemiology is the study of interacting species in which diseases spread. Theoretical research and field observations have established the prevalence of various infectious diseases amongst the majority of ecosystem populations. This has necessitated the study of the impact of epidemiological parameters in the ecological domain. On the other hand, delay is very common in many processes such as population dynamics and epidemiology. Unfortunately, not much has been done for delayed ecoepidemic models. This motivates the proposed research. In this project, some new delayed ecoepidemic models will be proposed. With existing and these newly built delayed ecoepidemic models as prototypes, we will study the local and global dynamics of some abstract delayed equations. In these equations, delay can be discrete, distributed, or state-dependent. We concern with the stability of equilibria, Hopf bifurcation, backward bifurcation, spreading speed, and travelling waves. Techniques like linearization, Lyapunov functional method, normal form theory, monotone operator theory will be employed. This will contribute greatly to the theory of delayed differential equations. Moreover, the theoretic results will be applied to concrete problems. We hope that the obtained results will be useful to guide public health policy decisions and to control infectious diseases.

生态流行病学是对疾病传播的相互作用物种的研究。理论研究和实地观察已经确定了大多数生态系统种群中各种传染病的流行。这就需要研究流行病学参数对生态领域的影响。另一方面，延迟在人口动态和流行病学等许多过程中非常常见。不幸的是，对于延迟生态流行病模型还没有做太多工作。这激发了拟议的研究。 在这个项目中，将提出一些新的延迟生态流行病模型。以现有的和新建的延迟生态流行病模型为原型，我们将研究一些抽象延迟方程的局部和全局动力学。在这些方程中，延迟可以是离散的、分布式的或与状态相关的。我们关注平衡点的稳定性、Hopf 分岔、后向分岔、传播速度和行波。将采用线性化、Lyapunov泛函方法、范式理论、单调算子理论等技术。这将对延迟微分方程理论做出巨大贡献。此外，理论结果将应用于具体问题。我们希望所获得的结果将有助于指导公共卫生政策决策和控制传染病。