A model fix gone wrong: investigation of an SIS model with saturating treatment. Issue 2 (7th February 2021)

• Record Type: Journal Article
• Authors: Nelson, Mark Ian
• Is Part Of: International journal of mathematical education in science and technology. Volume 52:Issue 2(2021)
• Page Start: 299
• Page End: 309
• Publication Date: 2021-02-07
• Subjects: Modelling -- SIS -- steady-state solutions -- units; 97M10; Mathematics -- Study and teaching -- Periodicals; Mathematics -- Periodicals; 510.07
• DOI: 10.1080/0020739X.2020.1745916
• Languages: English
• ISSNs: 0020-739X

Abstract

ABSTRACT: A textbook model of a contagious disease, the dynamics of which are represented by the SIS epidemic model with saturating treatment, is considered. I show that this model, as originally formulated, is not dimensionally consistent. The model can be fixed by including a dimensional constant a of value one (with units i n d i v i d u a l s − 1 ). At first sight, it appears that this is a cosmetic book-keeping exercise that will have no flow-on effects on the analysis of the model. In fact, we will discover that setting the value a = 1 i n d i v i d u a l s − 1 produces very unrealistic outcomes and that the parameter must have value a ≪ 1 i n d i v i d u a l s − 1 . Necessary skills for students to work through this model are an understanding of steady-state solutions and linearized stability for a scalar differential equation and, most importantly, an understanding of units.