Part A Differential Equations I and Modelling in Mathematical Biology. Part A Differential Equations II is also preferable but not necessary.
Further Mathematical Biology provides an introduction to more complicated models of biological phenomena, including spatial models of pattern formation and free boundary problems modelling invasion. The course focuses on applications where continuum, deterministic models formulated using ordinary and/or partial differential equations are appropriate, but also includes an introduction to discrete, stochastic models and how to relate them to continuum models. By using particular modelling examples in ecology, chemistry, biology and physiology, the course demonstrates how applied mathematical techniques, such as linear stability, phase planes and travelling waves, can yield important information about the behaviour of complicated models.
Students will have developed a sound knowledge and appreciation of the ideas and concepts related to modelling biological and ecological systems using ordinary and partial differential equations and been introduced to discrete stochastic models.
\(\bullet\) Non-spatial models with delays, including biological examples from population ecology and physiology.
\(\bullet\) Age-structured models with biological and physiological examples.
\(\bullet\) Introduction to spatial models, including morphogen gradients, chemotaxis and patterning.
\(\bullet\) Travelling wave propagation with biological examples, including Fisher’s equation and epidemics.
\(\bullet\) Biological pattern formation, including Turing's model for animal coat markings and chemotaxis models.
\(\bullet\) Moving boundary problems with biological examples, including colonisation and wound healing.
\(\bullet\) Discrete-to-continuum models, including space- and velocity-jump models for diffusion and chemotaxis.