Introductory description

This module will cover the main mathematical techniques currently being used to understand cancer and analysis of cancer data. Cancer can be viewed as a dynamical system, an ecology or an evolutionary process. A number of cancer modelling frameworks have been used depending on the problem, including deterministic compartmental ODEs, probabilistic models (eg branching processes), spatial or structured populations (PDEs, agent based simulations), each having particular merits. This module will present various models and how these are used to design therapy.

Module aims

Outline syllabus

This is an indicative module outline only to give an indication of the sort of topics that may be covered. Actual sessions held may differ.

1. Mathematical models of evolution and mutation. (branching process models of mutation and applications to cancer).
2. Cancer growth models.
3. Spatial modelling/structured modelling of tumours.
4. Optimisation of therapy.
5. Data analysis for cancer data.

Learning outcomes

By the end of the module, students should be able to:

• Acquire an understanding of cancer as an evolutionary process and the mutation process dependencies.
• Use of branching processes to quantify risk of drug resistant mutations.
• Optimisation techniques to determine optimal therapy schedules.

Interdisciplinary

This is a mathematics focused module on the life science interface. Students will be taught the necessary biology.

Subject specific skills

Ability to translate biological mechanisms into mathematical framework, eg growth processes.
Ability to analyses and solve stochastic and deterministic models of cancer.
Ability to apply optimisation methods to ODEs.

Transferable skills

Ability to translate scientific ideas into mathematical language and back. Ability to think creatively. Ability to discern the validity of a proposed explanation.