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A model fix gone wrong: investigation of an SIS model with saturating treatment

Journal Article


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 (Formula presented.)). 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 (Formula presented.) produces very unrealistic outcomes and that the parameter must have value (Formula presented.). 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.

Publication Date


  • 2021

Citation


  • Nelson, M. I. (2021). A model fix gone wrong: investigation of an SIS model with saturating treatment. International Journal of Mathematical Education in Science and Technology, 52(2), 299-309. doi:10.1080/0020739X.2020.1745916

Scopus Eid


  • 2-s2.0-85083662905

Start Page


  • 299

End Page


  • 309

Volume


  • 52

Issue


  • 2

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 (Formula presented.)). 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 (Formula presented.) produces very unrealistic outcomes and that the parameter must have value (Formula presented.). 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.

Publication Date


  • 2021

Citation


  • Nelson, M. I. (2021). A model fix gone wrong: investigation of an SIS model with saturating treatment. International Journal of Mathematical Education in Science and Technology, 52(2), 299-309. doi:10.1080/0020739X.2020.1745916

Scopus Eid


  • 2-s2.0-85083662905

Start Page


  • 299

End Page


  • 309

Volume


  • 52

Issue


  • 2