Modelling heterogeneities in disease transmission and predation

每个生态模型的核心，无论是否明确规定，都是关于个体之间遭遇率的假设：捕食者和猎物之间，宿主和寄生虫之间，植物和昆虫之间，或者感染和易感个体之间。 大多数模型假设个体是相同的，相互作用是独立的。 事实显然并非如此;个体几乎在每个方面都是异质的：行为，生理，大小，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，即使是个体的细微变化也会导致有趣和意想不到的结果。 这在疾病控制中尤其如此;疫苗接种模型可以在同质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。 本研究的目的是开发和测试建模方法的具体案例研究。 该研究主要包括三个方面的内容：发展几个特定系统的预测模型，发展和分析一般系统的理论模型，研究适用于疾病传播、空间传播和捕食者-被捕食者模型的分析技术，这些基础研究对农业、水产养殖业、林业以及公众健康都具有重要意义。 所要求的资金将用于为具体的农业和水产养殖系统开发模型。 两个看似不相关的例子包括翡翠灰螟的传播和流感的控制;然而，模型和模拟是环境和健康规划所有领域预测和控制的重要工具，因此研究将产生比这两个具体问题更广泛的影响。

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.The basic research suggested in this proposal is significant to the agriculture, aquaculture and forest industries as well as public health.  The funding requested will be used to develop models for specific agricultural and aquacultural systems.  Two seemingly unrelated examples include the spread of Emerald Ash Borer and the control of influenza; however, models and simulations are essential tools for prediction and control in all areas of environmental and health planning, and so the research will have a much wider impact than these two specific problems alone.