A Model Fix Gone Wrong: Investigation of an SIS Model with Saturating Treatment

Autor/in	Nelson, Mark Ian
Titel	A Model Fix Gone Wrong: Investigation of an SIS Model with Saturating Treatment
Quelle	In: International Journal of Mathematical Education in Science and Technology, 52 (2021) 2, S.299-309 (11 Seiten)Infoseite zur Zeitschrift PDF als Volltext Verfügbarkeit
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	0020-739X
DOI	10.1080/0020739X.2020.1745916
Schlagwörter	Textbooks; Models; Communicable Diseases; Epidemiology; Teaching Methods; Intuition; Thinking Skills; Genetics; Epistemology; Mathematical Models; Equations (Mathematics); Units of Study; Mathematics Instruction; Undergraduate Students; Intervention; Medical Services; Foreign Countries; Australia + Suchen Sie Ihr Suchwort? Textbook; Text book; Schulbuch; Lehrbuch; Analogiemodell; Contagious disease; Contagious diseases; Communicable disease; Infektionskrankheit; Epidemiologie; Teaching method; Lehrmethode; Unterrichtsmethode; Denkfähigkeit; Humangenetik; Erkenntnistheorie; Mathematical model; Mathematisches Modell; Equations; Mathematics; Gleichungslehre; Lerneinheit; Mathematics lessons; Mathematikunterricht; Arzt; Ausland; Australien
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 [alpha] of value one (with units individuals[superscript -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 [alpha]=1 individuals[superscript -1] produces very unrealistic outcomes and that the parameter must have value [alpha]<<1 individuals[negative 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. (As Provided).
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Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2022/1/01