Modelling heterogeneities in disease transmission and predation

每个生态模型的核心，无论是否明确规定，都是关于个体之间相遇几率的假设：捕食者和猎物之间，宿主和寄生虫之间，植物和昆虫之间，或受感染和易受影响的个体之间。大多数模型假设个体是相同的，交互是独立的。情况显然并非如此；个体在几乎所有方面都是不同的：行为、生理、体型、年龄。尽管如此，简单的模型已经非常成功：无论是作为理论基础还是作为应用工具。然而，异质性显然很重要，即使个体之间的细微差异也可能导致有趣和意想不到的结果。在疾病控制方面尤其如此；疫苗接种模型可以在同类情况下预测疾病的控制，但在更一般的情况下预测双稳态和滞后。这项研究的目的是为具体的案例研究开发和测试建模方法。拟议的研究遵循三个途径：开发几个特定系统的预测模型，开发和分析一般系统的理论模型，以及研究适用于疾病传播、空间传播和捕食者-猎物模型的分析技术。

At the core of every ecological model, whether specified clearly or not, are assumptions about the encounter rates between individuals: between predator and prey, host and parasite, plant and insect or infected and susceptible individuals. Most models assume individuals are identical and interactions are independent. This is clearly not the case; individuals are heterogeneous in almost every aspect: behaviour, physiology, size, age. Despite this, simple models have been very successful: both as theoretical foundations and as applied tools. Heterogeneities, however, are clearly important, and even subtle variations in individuals can lead to interesting and unexpected results. This is especially true in disease control; vaccination models may predict control of the disease in the homogeneous case, but predict bistabilities and hysteresis in the more general case. The objective of this research is to develop and test modelling approaches for specific case studies. The proposed research follows three avenues: development of predictive models for several specific systems, development and analysis of theoretical models for general systems and a study of analytical techniques applicable to disease transmission, spatial spread and predator-prey models.