A model fix gone wrong: investigation of an SIS model with saturating treatment
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Mark Ian Nelson [1]
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[1] University of Wollongong
University of Wollongong
Australia
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- Localización: International journal of mathematical education in science and technology, ISSN 0020-739X, Vol. 52, Nº. 2, 2021, págs. 299-309
- Idioma: inglés
- Texto completo no disponible (Saber más ...)
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Resumen
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 individuals−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 individuals−1 produces very unrealistic outcomes and that the parameter must have value a 1 individuals−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.
