Potential research projects
Fully funded PhD scholarship available: mathematical modelling of cell invasion
I have several other projects that would be suitable for Masters or PhD students. These are just some examples, and there are lots of projects available. If you are interested in studying any of these (or if you have your own idea for a project!), please get in touch with me. Scholarships are available for suitable PhD and Masters students. |  |
Combining size and species in marine ecosystems
There are two main paradigms for the study of ecosystems: food webs and size spectra. The traditional food web approach uses an individual's species as the main indicator of its feeding requirements. More recently, marine ecosystems have been characterised by the relationship between body mass and abundance: small organisms are much more abundant than large ones, and this relationship is usually quite predictable. In this framework, an individual's size, rather than its species, determines its feeding preferences. Increasingly, it is being recognised than both size and species are important factors, and it is not sufficient to consider one in isolation. This project will systematically investigate the effects of adding a size structure to traditional species-based models, or alternatively of introducing different species into a size spectrum model.This project would be suitable for a Masters or PhD student.
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Weed risk assessment and control
New weeds have to go through a number of stages before they become an invasive pest. These include introduction to a particular country or region, naturalisation (or "going wild") and becoming a pest with some negative economic or other impact. The number of species present in each of these categories typically decreases by a factor of approximately 10 from one stage to the next. This poses a dilemma for weed management agencies. Should they focus their limited resources on controlling a few established pests (which may be widespread and impossible to completely elimiate), or should they divert some attention to the many species in the earlier stages, in an attempt to nip potential weeds in the bud before they become a problem? This question can be approached in the context of a bioeconomic optimisation problem, with the goal of minimising the "cost" of the system, consisting of the monetary cost of control, plus the negative impacts of weeds in the environment. Formulating the problem demands knowledge of factors involved in weed invasion and control. But once this is done, finding the optimum solution is pretty straightforward mathematically and has the potential to provide a general strategic framework for weed managers. More details...This project would be particularly suitable for a Masters student.
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Epidemic spread on a network
Information on the spread of an epidemic through a population is often collected in the form of contact tracing data -- essentially a tree showing who passed the disease onto whom. A natural way to model the spread of an epidemic that complements this form of data is a network model: the population is represented as a network with each node representing an individual, and links between nodes representing social contacts. Different networks have different mathematical properties, such as the mean and variance of the number of contacts per individuals, and the level of clustering of connections. These properties can be crucial in determining the spread or extinction of the epidemic. This project will investigate the relationship between network properties and epidemic progress, comparing the results with standard SIR-type models.This project would be suitable for a Masters or PhD student.