Modelling disease dynamics with realistic population mixing patterns

经典的数学流行病模型假设个体随机相互接触。但是，对于许多疾病来说，病原体是通过密切接触者传播的，而不是随机发生的。对于这类疾病，群体接触可以通过接触网络来建模，接触网络是具有代表个体的节点和代表接触的边的图。它们适合于模拟长期异质性接触，并且在针对这种异质性的疾病干预策略的研究中是不可或缺的，例如接触者追踪和靶向疫苗接种。我建议研究以下三个问题的接触网络，使这种建模方法更适用。 1)在网络上对周期性流行病进行建模，并使用该模型研究季节性流感的动态和演变。此外，这一模式将有助于识别感染和传播风险高的个人。关于确定复发性流行病的特征的知识将用于模拟接种疫苗后不诱导免疫的疾病及其通过密切接触传播的疾病。 2)确定基于网络的传播的特征，如密切接触者，并研究观察到的疾病流行曲线（例如，埃博拉和流感），以确定接触网络是否是这些疾病的重要传播方式。我还将研究如何修正经典模型，使其能够更精确地应用于密切接触者传播的疾病。 3)在非随机接触网络上建立疾病动力学模型，其中接触是完全已知的。在一个小的社区，或相互连接的社区（如城市或农场）的个人可以代表这样的网络。然而，网络模型与经典模型在控制传染病发生的条件上存在差异。我建议在完全指定的接触网络上开发一个疾病动力学的数学模型，并调查这种差异的原因。这项研究也将揭示这种差异是否存在于经典的疾病模型，考虑或忽略宿主内的病原体动力学。 通过提出的研究项目，我们将更深入地了解疾病在网络上传播的机制，并使这种建模方法更适用于真实的疾病。我们将拥有一个比经典疾病模型更强大的工具，以研究针对人群接触模式的疾病干预策略。

Classical mathematical epidemic models assume that individuals randomly contact each other. However, for many diseases, pathogens are transmitted through close contacts, which do not occur randomly. For such diseases, population contacts can be modeled by contact networks, which are graphs with nodes representing individuals and edges representing contacts. They are suitable to model long term heterogeneous contacts, and are indispensable in the study of disease intervention strategies that target this heterogeneity, such as contact tracing and target vaccination. I propose to investigate the following three problems on contact networks to make this modelling approach more applicable. 1) Model recurrent epidemics on a network, and use the model to study the dynamics and evolution of seasonal influenza. In addition, this model will help identify individuals with high risk in infection and transmission. The knowledge on the features determining recurrent epidemics will be used to model the diseases that do not induce immunity after vaccination, and their spread through close contacts. 2) Identify the features of network-based transmissions, such as close contacts, and study observed epidemic curves of diseases (e.g., Ebola and influenza) to determine if contact network is an important mode of transmission for these diseases. I will also study how to correct classical models so that they can more precisely applied to diseases transmitted by close contacts. 3) Model disease dynamics on a nonrandom contact network which contacts are fully known. Individuals in a small community, or inter-connected communities (such as cities or farms) can be represented such networks. However, there is a discrepancy of the condition governing when an epidemic can take off between the network models and the classical models. I propose to develop a mathematical model for disease dynamics on a fully specified contact network, and investigate the cause of this discrepancy. This study will also reveal if such discrepancy exists in classical disease models that consider or neglect within-host pathogen dynamics. Through the proposed research projects, we will gain deeper understandings of the mechanisms of disease spread on networks, and make this modeling approach more applicable to real diseases. We will have a tool more powerful than classical disease models to study disease intervention strategies that target the contact patterns of a population.