Two Loops, Three Loops, or Four Loops: Pedagogic Issues in Explaining Basic Epidemic Dynamics

摘要

How many feedback loops, and of what type, control the behavior of an epidemic? This seemingly simple question arose on trying to relate the behavior of the epidemic model widely used in K-12 system dynamics to its three-loop feedback structure. A search of the literature discovered two-, three-, and four-loop versions of the basic epidemic model in introductory system dynamics materials. How can the same behavior be explained with such different feedback structures? Can they all be right? This paper analyzes the three basic model structures and discusses implications for system dynamics pedagogy. We conclude that either the two- or four-loop versions of the basic epidemic model are acceptable representations, with the two-loop version recommended for beginners; the three-loop version of the system is never correct. In addition, we suggest that the development of incorrect representations such as the three-loop epidemic model can be avoided if standard system dynamics modeling practice is followed. At a macro level, standard practice dictates first formulating a dynamic hypothesis to explain the observed behavior (rather than building models by "hooking stocks and flows together"); at a micro level, standard practice suggests avoiding multiple algebraic expressions within variables.