Modeling multi-group dynamics of related viral videos with delay differential equations

Abstract

Epidemic models have previously been employed to better understand the spread of internet content, such as individual viral videos. Motivated by geographical differences between viewing populations, as well as by multiple viral videos which are linked or related in some way, we propose a multi-group susceptible–exposed–infected–recovered–susceptible (SEIRS) delay differential equation epidemic model for the popularity evolution of viral videos. The model accounts for the multi-group environment via (in general, heterogeneous) networks of single-group SEIRS equations. Existence and stability conditions for disease-free and endemic equilibrium states are obtained, while numerical simulations demonstrate the emergence of non-symmetric endemic equilibrium states across the network — in the case of heterogeneous parameters. In order to demonstrate the effectiveness of our modeling approach, we compare solutions to our model with data obtained from coupled YouTube videos. Our results demonstrate that the inclusion of coupling between such videos allows for better agreement with data than considering each video in isolation. Such results suggest that the multi-group epidemic modeling approach including time delays and coupling between videos is a useful tool for understanding the dynamics of viral videos which are connected in some manner. While the proposed network SEIRS differential delay equation epidemic model was applied to viral video data, it may be applicable to a wide variety of internet content and, more generally, may be used to model information propagation within and between communities under the assumption of time delays in information propagation.