What is a mathematical model?

A mathematical model is a description of a system. Modellers use the language of mathematics, i.e. variables and equations, instead of texts or figures. In order to describe complex systems, like a human cell or a population of animals, you need to develop an understanding of the relevance and relationships of the different components of that system. 

The term mathematical model is very general. In its broadest sense, it includes everything from simple linear regressions (because there is an underlying mathematical assumption about the relationship between the parameters you are doing the regression on) to large language models (because they have an internal concept of how language works). 

In this course, we will focus on mechanistic mathematical models in biology. These are models that aim to describe the mechanisms of biological systems. Typically, they are developed using a combination of literature / expert knowledge and experimental data. Mechanistic mathematical models can be used to analyse how components of a biological system interact, aiming to understand the system’s overall behaviour. With advances in high-throughput data and network analysis, mechanistic mathematical models have become increasingly essential for studying complex biological systems, diseases, and drug responses.

The advantage of mechanistic mathematical models is that the parameters are interpretable (so we can understand what their biological meaning is). Types of mechanistic models include Boolean network models, difference equation models, and ordinary differential equation models – we will talk about all of these in this course. 

Since this course is entirely focused on mechanistic mathematical models, we will call them mathematical models from now on.