Stochastic modelling and statistical inference for epidemics in structured populations

拟议研究的目的是建立纳入重要人口异质性的随机流行病模型，以及分析和统计推断的技术。本文将考虑这类模型的两大类。第一类涉及传染病模型，其中受感染个体的严重程度及其未来传播的潜力由感染剂量的大小决定。更具体地说，将对具有轻度和严重两种感染严重程度的各种模型进行调查，首先是针对均匀混合的人口，然后是针对家庭社区。对于每个模型，将确定确定爆发是否可以建立的阈值参数，以及其他属性，例如爆发建立的概率和最终结果。将使用各种模型探讨疫苗接种如何影响疫苗接种者对有关疾病的易感性以及他们在感染后传播疾病的能力，从而探讨对疫苗接种策略的影响。在第二类模型中，感染的传播可以在高危人群中以三个不同的水平发生。一个例子是允许感染发生在家庭、学校和广大人群中的模式，每个地方的感染风险不同。这些模型在文献中相对较少探索，但在现实生活中的流行病和大流行规划中越来越重要。特别是，诸如关闭学校或限制旅行等控制策略的有效性在很大程度上取决于这些模型所描述的那种人口水平的混合。提出的研究旨在探索这些模型的统计推断和数据收集的基本问题，解决诸如从不同类型的数据中可以推断出什么的问题，以及三层混合模型在多大程度上比简单但不太现实的模型更有用。

The aim of the proposed research is to develop stochastic epidemic models that incorporate important population heterogeneities, together with techniques for their analysis and statistical inference. Two broad classes of such models will be considered.The first class is concerned with models for infectious diseases in which the degree of severity of infected individuals and their potential for future spread are determined by the size of the infecting dose. More specifically, various models with two severities of infection, mild and severe, will be investigated, first for a homogeneously mixing population and then for a community of households. For each model, a threshold parameter that determines whether or not an outbreak can become established will be determined, together with other properties, such as the probability that an outbreak does become established and the final outcome if it does. Implications for vaccination strategies will be explored, using a variety of models for how vaccination affects a vaccinee's susceptibility to the disease in question and their ability to spread the disease if they become infected.The second class of models is that in which the spread of infection can occur at three different levels within the at-risk population. An example would be a model in which infection is permitted to occur within households, within schools, and also in the population at large, with different risks of infection in each place. Such models are relatively underexplored in the literature, but are of increasing importance in real-life epidemic and pandemic planning. In particular, the efficacy of control strategies such as school closure or travel restrictions relies crucially on the kind of population-level mixing that such models describe. The proposed research aims to explore fundamental issues of statistical inference and data collection for such models, addressing such questions as what can be inferred from different sorts of data, and the extent to which three-level-mixing models are more useful than simpler, but less realistic, models.