Aims & Learning Objectives: Aims: The aim of the course is to introduce students to applications of partial differential equations to model problems arising in biology. The course will complement Mathematical Biology I where the emphasis was on ODEs and Difference Equations.
Objectives:
Students should be able to derive and interpret mathematical models of problems arising in biology using PDEs. They should be able to perform a linearised stability analysis of a reactiondiffusion system and determine criteria for diffusiondriven instability. They should be able to interpret the results in terms of the original biological problem.
Content: Topics will be chosen from the following:
Partial Differential Equation Models: Simple random walk derivation of the diffusion equation. Solutions of the diffusion equation. Densitydependent diffusion. Conservation equation. Reactiondiffusion equations. Chemotaxis. Examples for insect dispersal and cell aggregation.
Spatial Pattern Formation: Turing mechanisms. Linear stability analysis. Conditions for diffusiondriven instability. Dispersion relation and Turing space. Scale and geometry effects. Mode selection and dispersion relation.
Applications: Animal coat markings. "How the leopard got its spots". Butterfly wing patterns.
