Modeling the spread of infectious diseases on contact networks

拟议的研究计划旨在开发现实的数学模型，以研究诸如艾滋病毒和流感等疾病及其干预策略。对于探索人类接触异质性的干预策略（例如，优先接种疫苗和接触者追踪），经典的流行病模型难以适用，因为它们不切实际地假设社区中的每对个体都可以以相同的概率进行接触和传播疾病。另一方面，现实的人类接触可以用网络来表示，其中节点代表个人，边代表接触。然而，目前这种接触网络上疾病动力学的数学模型仅限于静态网络，而忽略了免疫力的丧失。因此，它们不适用于流感（丧失免疫力）和艾滋病毒（导致出生、死亡和移徙）等疾病及其干预策略（通过隔离个人和消除接触者来改变接触网络）。我将建立疾病在接触网络上传播的数学模型，包括出生、死亡、迁移和免疫力丧失。将推导出决定一种疾病能否在人群中出现的条件。这些条件对于设计最佳干预策略至关重要。拟议的模型将用于回答诸如大流行性流感毒株如何变成季节性的问题；我们应该针对谁进行抗病毒治疗；我们应该先给谁接种疫苗。

The proposed research program aims to develop realistic mathematical models to study diseases such as HIV and influenza and their intervention strategies. For intervention strategies that explore the heterogeneity in human contacts (e.g. prioritized vaccination and contact tracing), classical epidemic models are difficult to apply because they unrealistically assume that every pair of individuals in a community can make contacts and transmit diseases with the same probability. On the other hand, realistic human contacts can be represented by networks where nodes represent individuals and edges represent contacts. However, current mathematical models for disease dynamics on such contact networks are limited to static networks, and neglect loss of immunity. Thus they are not suitable for diseases like influenza (with loss of immunity) and HIV (with births, deaths and migration), and their intervention strategies (altering contact networks by isolating individuals and removing contacts). I will develop mathematical models for disease spread on contact networks, incorporating births, deaths, migration, and loss of immunity. The conditions that determine whether a disease can emerge in a population will be derived. These conditions are crucial to designing optimal intervention strategies. The proposed models will be applied to answer such questions as how pandemic influenza strains become seasonal; whom we should target for antiviral treatment; and whom we should first vaccinate.