Sutton Trust Summer School - Mathematical Sciences Stream

Mathematical, computational and statistical modelling play an important role in decision making, particularly when making decisions under uncertainty. The tasks that encompass mathematical, computational and statistical modelling are surprisingly varied, including for example

• the definition and analytical analysis of theoretical models;
• using computational approaches to find numerical solutions and explore the behaviour of models through simulation;
• informing models through data and using them to support decision making.

The summer school was designed to give students a taster of the various aspects of mathematical modelling through a combination of lectures, workshops and computer labs.

Differentiation, pictures and behaviour: In this session we investigated how biological models of bacteria growth can be described using ordinary differential equations (ODEs). We then used visualisations to explore the behaviour of these ODEs.

Solving differential equations with Python: In this computer lab we used the programming language Python to numerically determine the values of a derivative of a function. We then numerically explored the solution to a set of ODEs that describe a classic model in epidemiology, the so-called SIR model (S = susceptible, I = infective, R = recovered).

Probabilistic models for infectious diseases: This workshop demonstrated how to use data to find reasonable values for the parameters of an SIR model. We moved from the deterministic SIR model to probabilistic models for epidemics that make use of the Binomial distribution.

Simulating the spread of an infectious disease using cellular automata: This computer lab demonstrated how to use cellular automata to simulate the spread of an epidemic. A cellular automaton is a collection of cells arranged in a grid. Each cell changes state as a function of time, according to a defined set of rules driven by the states of neighbouring cells.

Control measures for infectious diseases: In the final session a Warwick researcher from the mathematical sciences presented their research work relating to the NHS COVID-19 app.