Analysis and statistical inference of infectious diseases systems, with a focus on transient dynamics and delays

传染病系统的分析和统计推断，重点关注瞬态动态和延迟

• 批准号: RGPIN-2016-06010
• 负责人: Magpantay, FeliciaMaria
• 金额: $ 2.4万
• 依托单位: Queen's University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2020
• 资助国家: 加拿大
• 起止时间: 2020-01-01 至 2021-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=710092
• 关键词: Analysis; statistical; inference; infectious; diseases

The objective of my proposed research program is to develop techniques in the mathematical and statistical analysis of infectious disease systems, with a focus on the following commonly observed, but under-examined phenomena: 1. Long-lasting transient dynamics that occur after sudden changes in the system. An example of this is the "honeymoon period," a long period of low incidence after the initiation of mass vaccination programs. This could last for decades and may be followed by a resurgence of the disease. The study of honeymoon periods and other slow transient dynamics are still in its early stages, because the focus of much study in mathematical ecology and general complex systems is on faster dynamics (e.g., epidemics) and small deviations from equilibria. 2. Complex dynamics resulting from the inclusion of feedback delays in disease systems, such as when members of a population change their contact rates in response to a disease outbreak, or when public health measures to reduce transmission are applied. These measures take time to be implemented depending on the urgency of the situation. As a result, the delays are "state-dependent," because they depend on the state of the outbreak. The study of state-dependent delay systems is new and challenging, but has many applications in many fields of science and engineering. This research will employ an integrated approach that spans analysis of both deterministic systems and stochastic processes, development of mechanistic model systems for ecological processes, practical considerations for epidemiology, and design of efficient statistical inference techniques for fitting model parameters to data. All analysis will begin with the formulation of a deterministic skeleton of the dynamics written as systems of ordinary, partial and delay differential equations. This way the basic features of the models can be distinguished from the equally important effects of stochasticity such as periodic fluctuations and resonance. Linearization techniques, numerical bifurcation methods, Lyapunov and pseudo-potential functions will be employed. The effects of demographic and environmental stochasticity will be considered. The stochastic models will be fit to data using modern statistical inference techniques, such as iterated filtering. This research program will also develop methods to estimate missing or incomplete covariates (such as vaccine coverage), efficiently consider multiple data sets, correctly propagate uncertainty in estimates and predictions, and fit models to general stochastic systems, including those with time delay. This research program will provide a foundation upon which many different types of models can be built, analyzed and challenged with data. With its multi-faceted approach, this program may be applied to phenomena and models of complex systems even beyond those in disease ecology.

我提出的研究计划的目标是开发传染病系统的数学和统计分析技术，重点关注以下常见但未被充分研究的现象： 1.在系统突然变化后发生的持久瞬态动态。其中一个例子是“蜜月期”，即大规模疫苗接种计划启动后的一段长时间低发病率。这可能会持续几十年，随后可能会出现疾病的死灰复燃。对蜜月期和其他缓慢瞬态动力学的研究仍处于早期阶段，因为数学生态学和一般复杂系统中的许多研究的重点是更快的动力学（例如，流行病）和小的偏离均衡。 2.由于疾病系统中包含反馈延迟而产生的复杂动态，例如当人口成员因疾病爆发而改变其接触率时，或当采取公共卫生措施以减少传播时。这些措施的实施需要时间，视情况的紧迫性而定。因此，延迟是“状态依赖性的”，因为它们取决于疫情的状态。状态依赖时滞系统的研究是一个新的、具有挑战性的课题，但在许多科学和工程领域有着广泛的应用。 本研究将采用一种综合的方法，跨越确定性系统和随机过程的分析，生态过程的机械模型系统的发展，流行病学的实际考虑，以及设计有效的统计推断技术拟合模型参数的数据。所有的分析将开始制定一个确定性的骨架的动力学写为系统的普通，偏微分方程和延迟微分方程。通过这种方式，模型的基本特征可以与同样重要的随机性效应（如周期性波动和共振）区分开来。将采用线性化技术、数值分叉方法、李雅普诺夫函数和伪势函数。将考虑人口和环境随机性的影响。随机模型将使用现代统计推断技术（如迭代过滤）与数据拟合。该研究计划还将开发方法来估计缺失或不完整的协变量（如疫苗覆盖率），有效地考虑多个数据集，正确传播估计和预测中的不确定性，并将模型拟合到一般随机系统，包括具有时间延迟的系统。 该研究计划将提供一个基础，在此基础上可以构建、分析和用数据挑战许多不同类型的模型。凭借其多方面的方法，该计划可以应用于复杂系统的现象和模型，甚至超越疾病生态学。