PhD title: modelling spatially extended disease interactions

Project summary:
Population structures are changing. Developments in mass transportation and family structure are modifying the mixing patterns of humans, while changes in farming practices are having a similar effect for agricultural populations. Inevitably, these changes mean that pathogens are no longer perfectly adapted and evolutionary change is catalysed, leading to the proliferation of novel strains or the emergence of new diseases. It is important that we therefore understand the likely impact of these altered population structures on the evolution of pathogen behaviour and disease virulence. The aim of the project is to use mathematical modeling to examine how different social and spatial characteristics of populations shape the evolution of their diseases.
Key objectives:
1) To develop a new theory of the evolution of virulence and other disease characteristics in complex structured host populations.

2) To use data to characterize the structure of realistic contact networks in terms of key parameters and thereby determine the role of such parameters in the evolution of pathogenic disease.

3) To make predictions of the changes in virulence that may be expected as diseases adapt in response to current changes in social/spatial structure of the population.
Classical theory of the evolution of parasites are underpinned by homogeneous mixing models. However, the assumption of homogeneous mixing in host populations ignores the fact that certain individuals are more likely to contact and therefore infect others. Despite this, there is no current analytical theory of phenotypic evolution in spatially/socially explicit populations. Indeed, the inclusion of such structure has so far only been included in simulation approaches or via spatially implicit moment closure schemes. A better theoretical understanding is important since a precise quantitative description could be very useful for the prediction of new disease outbreaks and the control of emergent diseases. To achieve the objectives of the project, the student will develop a new dynamical extension of evolutionary theory appropriate to social/spatial populations.

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Dr Steven D. Webb tel: +44 (0)141 5483803
Department of Mathematics fax: +44 (0)141 5483345
University of Strathclyde email: sdw@maths.strath.ac.uk<mailto:sdw@maths.strath.ac.uk>
Livingstone Tower web: http://www.maths.strath.ac.uk/~aas07104/index.html
26 Richmond Street office: L9.14
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Scotland, UK