Epidemiological dynamics in populations with demographic and spatial structure

传染病流行的动态是由传播驱动的，传播取决于接触，接触模式由个人之间的关系决定。这项研究的目标是使用数学模型来探索其中一些联系过程的作用，这些模型解释了人口中的空间和人口结构。这项研究的结果将加强我们对传染病传播的了解，并可能导致改进监测或控制策略。我们将使用集合种群框架将空间结构纳入我们的模型。前提是将种群视为相互关联但半自治的子种群的集合。这些亚群可以对应于城市或国家的区域，并通过临时(通勤)流动或永久(迁徙)流动结合在一起。通常，我们关注这些亚群的组成和耦合如何影响传染病的持久性和空间传播。我们将使用家庭框架将人口结构纳入我们的模型。在这里，总人口被视为一小群同居的个体。在对家庭内个人之间的互动进行建模时，随机效应很重要，因为我们考虑的是少数频繁和长时间接触的个人。由此产生的接触链通常被建模为马尔可夫过程。分析的重点是家庭组成和家庭之间的耦合如何影响流行病的风险。我们的目标是在集合人口和家庭模型框架中进一步发展流行病学动力学理论。我们的方法将结合对简单模型的数学分析、对更复杂模型的计算分析以及使用基于代理的模型的经验驱动的模拟。我们预计，最简单的模型将提供关键的见解，但不会捕捉到现实世界环境的一些重要方面。更现实的模型可能会变得相当复杂，我们将需要开发数字有效的方法来计算流行病学分析的基本指标，如繁殖数量。我们已经确定了两个初步项目。我们预计，这些将导致丰富的其他研究途径。在项目1中，我们将开发一个基于城市规模的家庭集合人口的框架。我们将把家庭分成空间上限定的子群体，并通过人员流动将这些子群体耦合在一起。我们假设，在许多城市，地区往往具有明显的人口特征，包括家庭规模分布。我们预计，这些特点，加上地区规模和与其他地区的混合模式，将影响传染病的风险、持久性和空间传播。蒙古的乌兰巴托可能就是一个很好的案例。我们正在与儿童基金会和蒙古国立大学的可能合作者接触。在项目2中，我们将开发一个基于家庭框架的病媒传播疾病流行病学模型。我们预计，在这一框架内，重要的是从人口数量和生活在那里的蚊子数量来考虑家庭的构成。我们假设，家庭之间的传播可以通过两种途径发生：(1)感染者拜访另一户家庭，并被易受感染的蚊子叮咬；(2)易感人群访问另一户户，并被传染性蚊子叮咬。这些途径可能会在流行病学动态中发挥不同的作用。登革热病毒可能是一个很好的研究案例。传播登革热的主要蚊子通常一生都呆在同一所房子里，可以被建模为居住者。

The dynamics of infectious disease epidemics are driven by transmission, transmission depends on contact and contact patterns are determined by the relationships between individuals. The goal of this research is to explore the roles of some of these contact processes using mathematical models that account for spatial and demographic structures within the population. The results of this research will enhance our understanding of the spread of infectious diseases and may lead to improved surveillance or control strategies. We will use a metapopulation framework to incorporate spatial structure into our models. The premise is to view the population as a collection of connected, but semi-autonomous, subpopulations. These subpopulations may correspond to regions of a city or country and be coupled via temporary (commuter) movement or permanent (migratory) movement. Typically, we are concerned with how the composition and coupling of these subpopulations impacts the persistence and spatial spread of the infectious disease.We will use a household framework to incorporate demographic structure into our models. Here, the total population is viewed as small groups of cohabiting individuals. Stochastic effects are important when modelling the interactions between individuals within the household because we are considering small numbers of individuals who share frequent and lengthy contacts. The resultant contact chains are often modelled as Markov processes. Analysis focuses on how household composition and the coupling between households impacts the risk of an epidemic.We aim to further develop the theory of epidemiological dynamics in metapopulation and household modelling frameworks. Our approach will combine mathematical analysis of simple models, computational analysis of more complex models, and empirically driven simulation using agent-based models. We anticipate that the simplest models will offer key insights, but will not capture some important aspects of the real world circumstance. More realistic models may become rather complex and we will need to develop numerically efficient methods for calculating essential metrics of epidemiological analysis such as reproduction numbers. We have identified two initial projects. We expect that these will lead to an abundance of other research avenues. In project 1 we will develop a framework based on a metapopulation of households on a city scale. We will group households into spatially delimited subpopulations, and couple these subpopulations by the movement of people. We hypothesise that, in many cities, districts often have distinct demographic characteristics, including the household size distribution. We expect that these characteristics, together with the district size and pattern of mixing with other districts will impact the risk, persistence, and spatial spread of infectious diseases. Ulaanbaatar in Mongolia may be a good case study. We are in contact with possible collaborators from UNICEF and The National University of Mongolia. In project 2 we will develop a model for vector-borne disease epidemiology based on the household framework. We anticipate that, in this framework, it will be important to consider the household composition in terms of the number of people and the number of mosquitoes living there. We hypothesise that transmission between households can occur through two routes: (1) An infectious person visits another household and is bitten by a susceptible mosquito who becomes infected, (2) a susceptible person visits another household and is bitten by an infectious mosquito. These routes will likely have different roles in the epidemiological dynamics. Dengue virus may be a good case study. The main mosquito that transmits dengue often remain within the same house throughout its life, and can be modelled as an inhabitant.