Improving inference of pathogen transmissibility and effects of interventions during epidemics.

研究背景传染病对植物、动物和人类造成的威胁是全球性的重大后果之一。通过公共卫生措施控制传染病是一个深入研究的领域（由于其有效性），特别是在流行病的早期阶段。自世纪之交以来，持续跟踪随时间变化的繁殖数R_t越来越有助于指导干预措施应如何随时间变化。R_t定义为在流行病发生时由传染性病例产生的继发病例的预期数量。这一统计数字表明针对特定病原体，为控制疫情所需采取的干预措施的规模（例如，为使病例数开始下降而必须预防的接触者比例）。给定完美的接触者追踪信息，推断与时间相关的繁殖数（在某一时刻）将与计算在某一时刻主要病例产生的次要病例的平均数量一样简单。重要的是要注意，我们需要实时估计来为决策提供信息，但这里描述的“完美信息”方法只能回顾性地生成。在现实中，这样的信息是不可用的，相反，R_t推断是使用两种类型的数据来估计的。一种数据类型是发病率（新症状病例数），而另一种数据类型涉及所有感染者-感染者对之间的流行病学延迟分布。理想情况下，第二个数据是产生间隔（从原发性感染到继发性感染的延迟分布），在这种情况下，发病率数据将与感染日期建立索引。在实践中，使用代代间隔（由于准确确定感染者何时被感染的复杂性和模糊性）。这就是所谓的“序列间隔”（感染者和感染者之间出现症状的延迟分布）。为了准确地推断出随时间变化的复制数，人们应该用症状发生的日期来索引发病率数据。广义上讲，有两种统计方法（[5]和[6]），大量研究的R_t推论都是基于这两种统计方法。这两种方法都使用贝叶斯推理技术来生成随时间变化的置信区间和R_t的期望。这个项目将包括在bbbb2010年开展的工作的基础上进行建设。准确和精确的R_t估计在流行病期间具有重要意义，因为它是公共卫生措施必要严格程度的主要指标。因此，缺乏准确或精确的估计可能导致在R_t被低估的情况下延迟控制疫情（导致过高的发病率和死亡率），或者相反，在R_t被高估的情况下采取不必要的公共卫生措施。目前，这些估计都不包括非静态（时间演变）序列间隔（感染者和感染者对症状发作之间的延迟分布）估计。有初步证据（[9],[11]）表明，时间演变的序列间隔可能对R_t估计有显著影响。目的：改进生成R_t估计的技术，并（在数学流行病学领域内）发展对时间变化序列间隔对R_t推断的意义（如果有的话）的理解。目的：建立一个关于变化序列区间的特征如何影响R_t推理的假设。调查真实世界的数据（最初来自刚果民主共和国北基伍省贝尼卫生区2018-2020年埃博拉疫情），在那里我可以推断生殖数量（有和没有更新序列间隔）来检验我的假设。扩展现有的R_t推断理论，将异质性纳入模型框架，例如空间/年龄模型

The context of the research *The threat that infectious diseases pose to plants, animals and humans is one of significant consequence globally [1]. Control of infectious diseases through public health measures is an intensely researched area (due to their effectiveness [2]), particularly during the early stage of an epidemic. Since the turn of the century, continual tracking of the time-dependent reproduction number, R_t, has increasingly become more helpful to guide how interventions should change through time. R_t is defined as the expected number of secondary cases generated by an infectious case once an epidemic is underway [3]. This statistic indicates the magnitude of the intervention required to control the outbreak (e.g. the proportion of contacts that must be prevented for cases numbers to begin falling), for the given pathogen. Given perfect contact tracing information, inferring the time dependent reproductive number (at timet) would be as simple as counting the average number of secondary cases that a primary case generates at time t. It is important to note that we require real-time estimates to inform decision making but the 'perfect information' approachdescribed here can only be generated retrospectively. In reality, such information is not available and instead, R_t inference is estimated using two types of data. One data type is incidence (number of new symptomatic cases), whilst the other concerns an epidemiological delay distribution between all infector-infectee pairs. The second piece of data would ideally be the generation interval (the distribution of delays from infection in a primary case to infection in a secondary case) and in which case the incidence data would be indexed to the date of infection. In practice, a proxy for the generation interval is used (owing to the complexity and ambiguity of determining exactly when an infectee becomes infected). This is the so-called the 'serial interval' (the distribution of delays between symptom onset in an infectorinfectee pair). To infer the time-dependent reproduction number accurately, one should then index the incidence data with date of symptom onset. Broadly speaking, there are two statistical methods ([5] and [6]) which a large number of studies base their R_t inferences on. Both of these methods use Bayesian inference techniques to generate time-evolving confidence intervals and expectations for R_t. This project will involve building on the work developed in [5]. Accurate and precise R_t estimation is of significance during an epidemic since it is the primary indicator of the necessary stringency of public health measures. Consequently, the lack of accurate or precise estimates can lead to either delays in bringing outbreaks under control (resulting in excess morbidity and mortality) in the event that R_t is under-estimated or conversely, unnecessary public health measures in the vent that R_t is over-estimated. Currently none of these estimates include non-static (time evolving) serial interval (the distribution of delays between symptom onset in an infectorinfectee pair) estimates. There is preliminary evidence ([9], [11]) to suggest that time evolving serial intervals may have a significant impact on R_t estimates.Aims: To improve the techniques that generate R_t estimates and to develop the understanding (within the field of mathematical epidemiology) about the significance (if any) of time varying serial intervals on R_t inference.Objectives:Develop a hypothesis on how characteristics of changing serial intervals will affect R_t inference.Investigate real world data (initially from the 2018-2020 Ebola epidemic in Beni Health Zone, North Kivu Province, DRC), where I can infer the reproductive number (with and without updating serial intervals) to test my hypothesis.Extend existing theory on R_t inference to incorporate heterogeneities into the model framework, e.g. spatial/age modelsExternal Partners - WHO