The aims of this course are to develop techniques of computational and differential equation modelling in biology, ecology and medicine. This will be done by a mixture of lectures on basic methodology, computer labs, case studies, and group-based modelling exercises. We will introduce a number of modelling approaches that are widely used in applications to the life sciences, including reaction-diffusion equations, age-structured models, multi-scale modelling, and integral representations of dispersal. The course will teach practical implementation of these modelling approaches in the context of computer simulations, which will be illustrated by prototype applications from biology, ecology and medicine. These methodologies will form the basis for a series of group-based modelling case studies.
1. Reaction-diffusion models (1.1 1. formulation of reaction-diffusion models and extensions to include advection and chemotaxis terms, 1.2 2. applications to pattern and wave phenomena in the life sciences 3. semi-arid vegetation and wound healing as prototype examples, 1.3 4. numerical solution via finite differences in one space dimension Crank-Nicolson method,implementation of boundary conditions)
2. Integral models for dispersal in ecology (2.1 1. basic approach, kernel selection, 2.2 2. thin- and fat-tailed kernels, 2.3 3. implementation in integrodifferential and integrodifference models, 2.4 4. invasions as a prototype application.)
3. Multiscale modelling in cell biology (3.1 1. cellular Potts model, 3.2 2. tumour angiogenesis as a prototype application)
4. Age- and stage-structured models in ecology (4.1 1. discrete time models with age and stage classes, 4.2 2. Leslie matrices, 4.3 3. continuous age- and stage-structured models)
5. Modelling case studies (5.1 1. group-based work on a mini-project, 5.2 2. group-based presentation, 5.3 3. individual written report)
By the end of the course, students should be able to do the following:
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SCQF Level: 11
Credits: 15