Effects of heterogeneity on population and epidemic dynamics

异质性对人口和流行病动态的影响

• 批准号: RGPIN-2019-05892
• 负责人: Chen, Yuming
• 金额: $ 1.38万
• 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: 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=758494
• 关键词: Effects; heterogeneity; population; epidemic; dynamics

Heterogeneity is an important factor in many biological processes. It can be spatial and/or temporal. Spatial heterogeneity refers to the uneven distribution of various concentrations of each species within an area. There are two kinds of spatial heterogeneity: patch structure and spatial diffusion. Temporal heterogeneity, for example, reflects the differentiation in the susceptibility and infectivity in epidemic and viral dynamics. Moreover, in the spread of diseases, behaviors of the human being and contacts among each other have obvious heterogeneity due to the evolution of society. Modeling heterogeneity will undoubtedly yield some new dynamical systems, which are very challenging to deal with. The purpose of this research program is to understand the effects of heterogeneity on the dynamics of some population and epidemic models.  With better understanding of the mechanisms underlying processes on population evolution and disease/virus spread, we shall modify existing models and propose new models to incorporate heterogeneity. The models may be described by ordinary differential equations, delay differential equations, reaction-diffusion equations, and ordinary differential equations coupled with first-order partial differential equations. In addition, most of the models are high dimensional or infinitely dimensional dynamical systems and hence usually are quite difficult to study. We shall use existing theory of dynamical systems and develop new techniques to tackle these problems. Expected results include the well-posedness of the systems, existence and stability of steady states, asymptotical spread speeds, traveling waves, backward bifurcation, Hopf bifurcation, among others. Based on these results, we will further analyze the effects of heterogeneity on the dynamics of such models. This study will not only lead to advancements in the theory of applied dynamics but also provide guidelines for policy makers to draw appropriate and effective strategies in disease control and resource management. Moreover, it will enhance the training of HQP and further our collaborations.

异质性是许多生物过程中的重要因素。它可以是空间和/或临时的。空间异质性是指一个区域内各种物种的各种浓度的分布不均匀。空间异质性有两种：斑块结构和空间差异。例如，时间异质性反映了流行病和病毒动力学的敏感性和感染的分化。此外，在疾病的传播中，由于社会的发展，人类和彼此之间的行为具有明显的异质性。建模异质性无疑会产生一些新的动态系统，这些系统非常挑战。该研究计划的目的是了解异质性对某些人群和流行模型的动态的影响。有了更好地了解种群进化和疾病/病毒扩散过程的基本机制，我们将修改现有模型和建议新模型以纳入异质性。这些模型可以用普通微分方程，延迟微分方程，反应扩散方程和普通微分方程以及一阶部分微分方程的普通微分方程来描述。此外，大多数模型都是高维或无限维动力系统的，因此通常很难研究。我们将使用现有的动态系统理论并开发新技术来解决这些问题。预期的结果包括系统的适当性，稳态的存在和稳定性，不对称的扩散速度，行进波，向后分叉，HOPF分叉等。基于这些结果，我们将进一步分析异质性对此类模型动力学的影响。这项研究不仅会导致应用动态理论的进步，而且还为决策者提供了指南，以制定疾病控制和资源管理方面的适当有效策略。此外，它将增强HQP的培训并进一步我们的合作。