Biology is undergoing a quantitative revolution, generating vast quantities of data that are analysed using bioinformatics techniques and modelled using mathematics to give insight into the underlying biological processes. This module aims to give a flavour of how mathematical modelling can be used in different areas of biology.
Typically the models that are used in biology cannot be solved analytically. Nonetheless they give very useful information about the behaviour of the system. We will start by studying what we can say about differential equations that we cannot solve. For example, we cannot solve the equation of a simple pendulum analytically, but we can still say under what conditions it has periodic solutions. For biological oscillators this is usually what matters: it is important that your heart beats regularly, but whether your pulse rate is 68 or 71 beats per minute is less critical.
Having introduced the mathematical tools needed to study ordinary differential equations, we will apply them to simple models of population dynamics, epidemics and biochemical reaction networks.
One of the pre-requisites for MATH6149
Pre-requisites: MATH1059 AND MATH1060