Mathematical models in epidemiology

2002-2003年的SARS疫情和预期的可能的流感大流行引起了对流行病的数学模型的注意。一种方法是基于假设的结构化人口和联系人结构执行许多随机模拟。另一种方法是分析相对简单的确定性划分模型。每种方法都有其优点和缺点。我们计划与分区模型合作，在疾病暴发之前提出管理策略，根据可获得的数据数量和可靠程度，制定不同复杂性和结构的模型。最终目标是决定对于给定的流行病知识状态，使用哪种模型是最合适的。要研究的模式包括对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，以及减少接触者的教育。我们还希望结合网络科学的新发展来模拟流行病的过程，在这个过程中，网络随着流行病的进展而变化。我们希望能够比较不同管理策略的效果，并尝试进行优化。一个例子是，集中对接触较少但更易受感染的人进行流行前疫苗接种是更好的做法，还是对更活跃、不那么脆弱的人更好。将这种模型的预测与更高度结构化的模型的预测进行比较，可能会深入了解管理战略的重要考虑因素是什么。

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.