Research Interests

I have two main themes to my research:

• transient effects in ecological systems

• modelling the effect of public health provision on the spread of infectious diseases

Transience

Recently, there has been growing interest in transient behaviours of ecological systems from the theoretical ecology community. Determining conditions for invasion of new or mutant species into a system and the progress of disease within a population are both examples of problems which have been addressed using mathematical models and which have an element of transience implicit in them. More generally, I am interested in any ecological system where there is regular disturbance or perturbation to the dynamical interaction between and within populations which means that the populations fail to reach any equilibrium.

In most cases, these transient interactions will occur in a spatial context. My preliminary work, in collaboration with Chris Gilligan, Plant Sciences Cambridge, on transient behaviours in a host pathogen system [1] indicated the importance of spatial structure on disease transmission profiles. In particular we were able to

·      assess the impact of initial pathogen distribution on disease transmission and

·      classify different types of pathogenic disease which are observed in agricultural systems in terms of the relative importance of dynamical interaction versus disease movement patterns.

I have received a Leverhulme Research Fellowship to continue this work, extended to consider problems of control of an invading species, and the effect of positive feedback on transient behaviours in a range of ecological problems. Some of this work will be in collaboration with Mike Neubert, Woods Hole and Rene van der Val (invasion of tree mallow in southeastern Scotland).

Infectious diseases

I am interested in how public health strategies and constraints impact on the spread and persistence of infectious diseases. This work has arisen from collaboration with clinicians working in the Milne Centre for sexually transmitted infections, Bristol, UK. The main contact, Dr. Dushyant Mital, is now working at Milton Keynes General Hospital. Bristol is a major, cosmopolitan UK city with a very high young person population. Unlike many other cities, the healthcare provision for STI and HIV in Bristol is undertaken at 2 separate sites. Moreover, the Milne centre is not able to see all patients straight away. The questions which arise from this situation include:

• How does the waiting time for an appointment affect infection levels in the Bristol population?

• How does healthcare provision at two locations affect infection levels of STI and HIV?

Other related questions involve how population structure impacts on disease transmission and for this, we can subdivide the population into different groups which can be categorised according to their sexual activity level and fidelity and their natural susceptibility to infection. I would be interested to hear from others working in the field of infectious diseases to see whether there are further modelling opportunities.

Studentship opportunities

I welcome enquiries from individuals who would like to discuss the possibility of research in these areas. I offer MSc projects (with a more diverse portfolio of problems) and PhD projects linked to my main interests. There is an earmarked PhD studentship in Mathematical Biology available from October 2007.

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