Stochastic modelling and statistical inference for epidemics in structured populations

拟议的研究的目的是开发随机流行病模型，将重要的人口异质性，以及他们的分析和统计推断的技术。将考虑两大类这样的模型：第一类是关于传染病的模型，其中受感染个体的严重程度及其未来传播的可能性由感染剂量的大小决定。更具体地说，将研究具有两种严重程度感染（轻度和重度）的各种模型，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，将确定一个阈值参数，该参数决定是否可以建立一个爆发，以及其他属性，如爆发确实建立的概率和如果建立的最终结果。疫苗接种策略的意义将被探讨，使用各种模型，疫苗接种如何影响接种者对疾病的易感性和他们的能力，如果他们成为感染疾病的传播。第二类模型是，其中感染的传播可以发生在三个不同的水平在风险人群。一个例子是一个模型，在这个模型中，感染被允许发生在家庭内部、学校内部以及整个人口中，每个地方的感染风险都不同。这些模型在文献中相对较少，但在现实生活中的流行病和流行病规划中越来越重要。特别是，控制策略的有效性，如学校关闭或旅行限制，关键取决于这种模型所描述的人口水平的混合。拟议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，以及三级混合模型比简单但不太现实的模型更有用的程度等问题。

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.