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

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.