Modelling heterogeneities in disease transmission and predation

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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.