Robust Mathematical Modelling of Household-Stratified Epidemic Time-series

传染病影响我们所有人，是全世界人类健康和生活质量的主要风险之一。尽管我们对它们的理解有所进步，但关于传染病实际上通过人群传播的方式，仍然存在许多问题。一些悬而未决的问题，即使是像流感这样的常见疾病，也涉及到对相当基本的数量的估计：疾病在不同情况下的传染性有多大;不同年龄的病例的传染性有多长;康复后对再次感染的免疫力有多大;其他更基本的问题涉及更微妙的问题。许多人类病原体物种被区分为可以使用现代实验室技术识别的菌株，但这些菌株相互作用的方式-例如，先前感染一种菌株是否会赋予另一种菌株免疫力-是复杂的，难以确定。与此同时，疾病的严重程度和传染性之间的关系可能相当复杂，要解决这些问题和其他问题，需要研究疾病在自然环境中的传播，但仅仅测量人口中的疾病数量并不能产生足够的信息来解决这些问题。进行一项家庭队列研究，包括测量几个家庭的感染情况，可以提供更多的信息。这类研究越来越频繁，本项目旨在开发分析住户队列研究所需的数学方法，以便尽可能多地提取新的流行病学信息。有几个步骤需要采取：第一个问题可能是，如果我们知道每一个相关的数量，那么一组给定的研究结果被观察到的可能性有多大。通过创造在计算机上有效计算这一数量的方法，可以逆转这一过程，并深入了解产生数据的流行病学机制，最终，通过更多地了解疾病在人群中传播的方式，我们可以改善对疾病的控制。例如，如果一种疾病的新病例在几天内没有传染性，那么这就为检疫提供了时间，使其成为一种有效的控制措施。如果家庭内传播比家庭间传播严重得多，那么干预措施应侧重于家庭。

Infectious diseases affect us all, and are one of the main risks to human health and quality of life worldwide. Despite advances in our understanding of them, a great many questions remain about the way in which infectious diseases actually transmit through human populations. Some open questions, even for common diseases like influenza, relate to estimation of quite basic quantities: how infectious is the illness in different contexts; how long cases of different ages are infectious for; and how much immunity to re-infection is conferred upon recovery.Other more fundamental questions relate to more subtle issues. Many human pathogen species are differentiated into strains that can be identified using modern laboratory techniques, but the way that these interact with each other - for example, whether previous infection with one strain confers immunity to another - is complex and hard to determine. At the same time, the relationship between severity of illness, and how infectious as case is, can be quite complex.Answering these and other questions requires study of disease transmission in a natural setting, but simply measuring the amount of illness in a population does not yield sufficient information to resolve them. Conducting a household cohort study, which involves measuring infections in several whole households over time, offers the promise of much more information. Such studies are being run with increasing frequency.This project is about developing the mathematics needed to analyse household cohort studies in a way that extracts as much novel epidemiological information as possible. There are several steps to be taken: a first question might be how likely a given set of study results are to be observed if we knew every relevant quantity. By creating methods to calculate such a quantity efficiently on a computer, it can become possible to invert the process and gain insight into the epidemiological mechanisms that generate the data.Ultimately, by knowing more about the way in which diseases spread through the human population, we can improve our control of them. For example, if new cases of a disease do not become infectious for several days, then this gives time for quarantine to be an effective control measure. If within-household transmission is much more intense than between-household transmission, then interventions should be focused on the household.