In March 2021 NRICH Dr Ems Lord joined forces with Anita Simpson from the Dover Grammar School for Girls to explore the potential of mathematical modelling to enthuse future mathematicians as part of the Subject Passion as a Teaching Tool lectures - an exciting collaboration between Trinity College at the University of Cambridge and World Class Schools.
On this page you'll find links to various NRICH activities highlighted by Ems during her talk and the accompanying Using A Level maths to model the spread of infectious disease materials prepared by Anita.
*Schools are encouraged to share examples of their students' work using the resources on this page. To do so, please click on the 'Submit a Solution' tab. Deadline for submission is 30th April 2021. A selection of the submitted solutions will be published on this page.*
Modelling takes students on the next steps in their problem-solving journey. Building models is a fascinating experience but it also takes students out of their comfort zones by challenging them to make assumptions, prioritise and justify their decision making. The slides accompanying the live webinar are here.
Students can experience exponential growth for themselves by playing The Standing Disease game which was devised by University of Cambridge researchers working with secondary students as part of a public engagement project.
This exponential growth is explored in the first section of Anita's Using A Level maths to model the spread of infectious disease materials.
We can safely investigate the spread of diseases across social networks using the activity Epidemics on Networks which was also developed by the researchers as part of a public engagement project. This was achieved by looking at how individuals interacted with one other (who came into contact with whom, and how often). Mathematical modellers can then build this into their simulations to understand how an outbreak has spread through a population. This is vital for health researchers to understand, as it helps them to to contact trace individuals who may have become infected, so as to stop an outbreak spreading further.
Although a simple exponential model holds surprisingly well for some situations, researchers have found that introducing other factors - such as the availability of food and living space (known as 'the carrying capacity' of an ecosystem) or whether someone is immune to an illness - can improve the accuracy of the models.
For animal populations, A Level students can explore models of increasing complexity here.
Students can also explore the spread of infectious diseases by investigating the S-I and S-I-R models in the accompanying Using A Level maths to model the spread of infectious disease materials.