Study of some systems from population dynamics and disease transmission dynamics with heterogeneity

从具有异质性的群体动态和疾病传播动态研究某些系统

• 批准号: RGPIN-2022-04744
• 负责人: Zou, Xingfu
• 金额: $ 2.26万
• 依托单位: University of Western Ontario
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2022
• 资助国家: 加拿大
• 起止时间: 2022-01-01 至 2023-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=758610
• 关键词: Study; some; systems; population; dynamics

This proposed research program consists of two parts. (A) Study spatial temporal dynamics of two classes of systems under spatially shifting heterogeneity that may account for environment/resource shifting caused by climate change or industrialization. One class are scalar delay differential equations for mature populations with maturation delay, and the other class are systems for population dynamics of interacting species including competing species and predator-prey species. (B) Explore various fear effects in predator-prey systems and the corresponding notion of fear effects in transmission dynamics of infectious diseases. For (A), the focus will be on how the shifting speed and the profile, together with the biological characteristics of the species involved, will affect the spatial temporal dynamics of governing systems. These characteristics include the type of birth functions, death rate, maturation delays, and type of interaction, rate of dispersal  and strengths of interaction. The possible topics include extinction/persistence, pattern of coexistence, spreading speed, pushed traveling waves and their stability, and impact of initial distribution. We will encounter some new dynamical systems with a special type of spatial-temporal heterogeneity with delay. I expect to develop some new approaches/methods, abd to modify and improve some existing ones to achieve our objectives. Thus, the results may contribute to the theory and methods for spatial dynamical systems, and they may also help understand the impact of climate change and industrialization. Part (B) is real world problem driven. We extend the notion of "fear effects" in predator-prey (P-P) systems to "susceptible-infectious" (S-I) interactions in modeling transmission dynamics of infectious diseases to reflect the reality that during the epidemic of an infectious disease, human beings behaviors (e.g., social activities and travel) will change and such changes are due to the fear of disease and may evolve with the epidemic. The focus in this part will be on how a prey's dispersal, foraging and production strategies evolve in response to perceiving its predator(s); and how human being's precaution level will evolve and the impact of such an evolution of precaution level on the long term and short term disease dynamics. I expect the results of this proposed research will have potential applications in agriculture and public health: the results on fear effect in P-P system may suggest new and environmentally friendly approaches for controlling some agriculture rodent pests; and the results on "fear effects" (e.g. represented by media coverage and public health agents' warning) on human's behavior change and its impacts may help inform decision makers,  in public health,  of valuable guidelines for controlling or mitigating the epidemics of an infectious disease.

这项拟议的研究计划由两部分组成。(A)研究两类系统在空间转移异质性下的时空动力学，这可能是气候变化或工业化造成的环境/资源转移的原因。一类是具有成熟时滞的成熟种群的标量时滞微分方程，另一类是相互作用的种群动力学系统，包括竞争种群和捕食-被捕食种群。(B)探讨捕食者-被捕食者系统中的各种恐惧效应，以及传染病传播动力学中恐惧效应的相应概念。对于(A)，重点将放在转移速度和轮廓以及所涉物种的生物特征将如何影响调控系统的时空动态上。这些特征包括出生功能的类型、死亡率、成熟延迟、相互作用的类型、分散率和相互作用的强度。可能的主题包括灭绝/持续、共存模式、传播速度、推动行波及其稳定性，以及初始分布的影响。我们将会遇到一些新的具有特殊时空异质性的时滞动力系统。我希望开发一些新的途径/方法，并修改和改进一些现有的方法，以实现我们的目标。因此，研究结果可能有助于空间动力系统的理论和方法，也可能有助于理解气候变化和工业化的影响。(B)部分是现实世界问题驱动的。在建立传染病传播动力学模型时，我们将捕食者-食饵(P-P)系统中“恐惧效应”的概念推广到“易感-传染病”(S-I)相互作用中，以反映在传染病流行期间，人类的行为(如社会活动和旅行)会发生变化，这种变化是由于对疾病的恐惧，并可能随着疾病的流行而演变。这一部分的重点将集中在猎物的扩散、觅食和生产策略如何随着对捕食者的感知而演变(S)；人类的预防水平将如何演变，以及这种预防水平的演变对长期和短期疾病动态的影响。我预期这项拟议研究的结果将在农业和公共卫生方面有潜在的应用：关于P-P系统中恐惧效应的结果可能会为控制一些农业啮齿动物害虫提供新的、环保的方法；以及关于“恐惧效应”(例如，通过媒体报道和公共卫生机构的警告)对人类行为变化及其影响的结果可能有助于为决策者，尤其是公共卫生部门的决策者提供有价值的指导方针，以控制或减轻传染病的流行。