Modelling disease dynamics with realistic population mixing patterns

经典的数学流行病模型假设个体之间是随机接触的。然而，对于许多疾病，病原体是通过密切接触传播的，这不是随机发生的。对于这类疾病，群体接触可以通过接触网络建模，接触网络是节点代表个体、边代表接触者的图。它们适合模拟长期异质性接触，并且在研究针对这种异质性的疾病干预策略（如接触者追踪和目标疫苗接种）中不可或缺。我建议在接触网络上研究以下三个问题，以使这种建模方法更适用。******1)建立网络上复发性流行的模型，并利用该模型研究季节性流感的动态演变。此外，该模型将有助于识别感染和传播风险较高的个体。关于决定复发性流行病特征的知识将用于模拟接种疫苗后不引起免疫的疾病及其通过密切接触传播的疾病。******2)明确密切接触等网络传播特征，研究观察到的疾病流行曲线（如埃博拉、流感），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，使它们能够更精确地应用于密切接触者传播的疾病。******3)在接触完全已知的非随机接触网络上建立疾病动力学模型。小型社区或相互连接的社区（如城市或农场）中的个人可以代表这种网络。然而，网络模型与经典模型在流行病爆发的条件上存在差异。我建议在一个完全指定的接触网络上建立一个疾病动力学的数学模型，并研究这种差异的原因。本研究还将揭示在考虑或忽视宿主内病原体动力学的经典疾病模型中是否存在这种差异。******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。我们将有一个比经典疾病模型更强大的工具来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.