APs, GPs and vCJD
Derwin Lawson · Teaching Mathematics and its Applications An International Journal of the IMA · 2001
When modelling the growth of any quantity the two simplest models assume either constant growth (where the same amount of new material is added in every time period) or proportionate growth (where the amount of new material in a time period is proportionate to the amount of material already present). For discrete models these growth assumptions lead to, respectively, arithmetic progressions and geometric progressions. The analysis of these sequences is accessible to A level students. It is also a very simple matter to implement such models within a spreadsheet. This allows easy investigation of the models and their sensitivity to parameter values. In this paper we describe an investigation of the applicability of these models to the onset on vCJD in humans. One of the important features of this investigation is that it demonstrates how simple mathematical techniques can sometimes allow a surprisingly robust qualitative conclusion to be drawn using sparse initial data. Given the restricted mathematical techniques required, this makes a powerful introduction to the use of mathematical models, which can be studied during the first week of an undergraduate career.