Abstracts of Paper's Published in 2021
In the following:
- a superscript p denotes an author
who was a PhD student at the time the research was carried out.
- a superscript u denotes an author
who was an undergraduate at the time the research was carried out.
- Mark Ian Nelson.
A model fix gone wrong:
investigation of an SIS model with saturating treatment.
International Journal of Mathematical Education in Science and
Technology, 52(2), pages 299-309, 2021.
https://doi.org/10.1080/0020739X.2020.1745916.
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 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
linearised stability for a scalar differential equation and, most importantly,
an understanding of units.
Keywords: Modelling, SIS, steady-state solutions, units.
Mark Ian Nelson.
A model fix gone wrong: investigation of an SIS model with saturating
treatment.
International Journal of Mathematical Education in Science and
Technology, 52(2), pages 299-309, 2021.
https://doi.org/10.1080/0020739X.2020.1745916.
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Page Created: 26th April 2021.
Last Updated: 21st April 2021.