Understanding digital platform evolution using compartmental models

Abstract

Due to the growing impact of digital platforms, it is increasingly important to understand their evolution through mathematical models. As their value is dependent on their user base, we present an improved perspective on modeling the number of users. Modeling digital platforms is frequently constrained by the scarcity of available data. Thus, researchers resort to open access data like Google Trends. We provide a new interpretation of such data, using it as a proxy for the demand, in contrast with the previous method of considering it as the active user-base. This is implemented using compartmental methods, in which the expression of the demand is fitted to the number of Google Searches for a specific keyword. Two cases, the MMO World of Warcraft and Facebook are analyzed in this fashion, using two different compartmental models. The solutions given by both models replicate key features of the real evolution of the services at study, and the parameters of the fit are in accordance with the expected relative values.