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

研究背景 * 传染病对植物、动物和人类构成的威胁是全球性的重大后果之一[1]。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[2]），特别是在流行病的早期阶段。自进入世纪以来，持续跟踪随时间变化的再生产数量R_t越来越有助于指导干预措施如何随时间变化。R_t定义为一旦发生流行病，传染病病例产生的继发病例的预期数量[3]。这一统计数字表明了为控制特定病原体的暴发所需干预措施的规模（例如，为使病例数开始下降而必须预防的接触比例）。给定完美的接触者追踪信息，推断时间依赖的繁殖数（在时间t）将与计算原发病例在时间t产生的继发病例的平均数一样简单。重要的是要注意，我们需要实时估计来告知决策，但这里描述的“完美信息”方法只能追溯性地生成。在现实中，这样的信息是不可用的，而是，R_t推断估计使用两种类型的数据。一种数据类型是发病率（新的有症状病例的数量），而另一种数据类型涉及所有感染者-被感染者对之间的流行病学延迟分布。理想情况下，第二部分数据是世代间隔（从原发病例感染到继发病例感染的延迟分布），在这种情况下，发生率数据将索引到感染日期。在实践中，使用了代间的替代（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“连续间隔”（感染者与被感染者之间症状发作延迟的分布）。为了准确地推断时间依赖的繁殖数量，应该用症状发作的日期索引发病率数据。广义地说，有两种统计方法（[5]和[6]）是大量研究的R_t推断的基础，这两种方法都使用贝叶斯推断技术来生成R_t的随时间变化的置信区间和期望。该项目将涉及在[5]中开发的工作的基础上。在流行病期间，准确和精确的R_t估计是重要的，因为它是必要的公共卫生措施的严格性的主要指标。因此，如果R_t估计过低，缺乏准确或精确的估计可能会导致控制疾病爆发的延误（导致发病率和死亡率过高），或者相反，在R_t估计过高的喷口采取不必要的公共卫生措施。目前，这些估计值都不包括非静态（时间演变）序列间隔（感染者与被感染者对中症状发作之间的延迟分布）估计值。初步证据（[9]，[11]）提出时间演变序列间隔可能对R_t估计有显著影响。目的：改进产生R_t估计的技术，加深对R_t估计的理解（在数学流行病学领域内）关于时变序列间隔对R_t推断的意义（如果有的话）。目的：提出一个假设，说明改变序列间隔的特征将如何影响R_t推断。调查真实的世界数据（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），我可以推断出（有和没有更新序列间隔）来检验我的假设。扩展现有的R_t推理理论，将异质性纳入模型框架，例如空间/年龄模型外部伙伴-卫生组织

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