Mathematical models in epidemiology

2002- 2003年的非典型肺炎流行和预期可能出现的流感大流行引起了人们对流行病数学建模的关注。一种方法是基于假设的结构化种群和接触结构进行许多随机模拟。另一种方法是分析相对简单的确定性隔间模型。每种方法都有其优点和缺点。我们计划使用分区模型，在疾病爆发之前提出管理策略，根据可用数据的数量和可靠性制定不同复杂性和结构的模型。最终目标是决定哪种模型最适合用于给定的关于流行病的知识状态。待研究的模式包括对已有治疗方法的疾病进行疫苗接种或抗病毒治疗，对尚未有治疗方法的新疾病进行检疫和隔离，以及开展减少接触的教育。我们还希望结合网络科学新发展的思想来模拟流行病的过程，其中网络随着流行病的发展而变化。我们希望能够比较不同管理策略的效果，并尝试优化。一个例子是，在流行前集中接种疫苗是针对不太可能有很多接触但更容易感染的人，还是针对更活跃但不那么容易感染的人。这种模型的预测当然取决于正在建模的疾病的参数，将其与更高度结构化的模型的预测进行比较，可能会让我们了解管理策略的重要考虑因素。

The SARS epidemic of 2002-3 and the anticipated possible influenza pandemic have drawn attention to the mathematical modelling of epidemics. One approach has been to perform many stochastic simulations based on an assumed structured population and contact structure. Another approach has been to analyze relatively simple deterministic compartmental models. Each approach has its advantages and disadvantages. We plan to work with compartmental models to suggest management strategies in advance of a disease outbreak, formulating models of different complexity and structure depending on how much and how reliable data are available. The ultimate goal is to decide what kinds of models are most appropriate to use for given states of knowledge about an epidemic. The models to be studied include vaccination or antiviral treatment for diseases for which treatment is available, and quarantine and isolation for new diseases for which treatments are not yet available, as well as education to reduce contacts. We hope also to incorporate ideas from the new developments in network science to model the course of an epidemic in which the network changes as the epidemic progresses. Our hope is to be able to compare the effects of different management strategies and to try to optimize. One example is the question of whether it is better to concentrate on the pre-epidemic vaccination on people less likely to have many contacts but more vulnerable to infection or on more active less vulnerable people. Comparison of predictions of such a model, which would certainly depend on the parameters of the disease being modelled, with those of a more highly structured model might give insights into what are the important considerations for management strategies.