Quantitative analysis of social influence and digital piracy contagion with differential equations on networks.

Illegal file sharing of copyrighted contents through popular file sharing networks poses an enormous threat to providers of digital contents, such as, games, softwares, music and movies. Though empirical studies of network effects on piracy is a well-studied domain, the dynamics of peer effect in the context of evolving social contagion has not been enough explored using dynamical models. In this research, we methodically study the trends of online piracy with a continuous ODE approach and differential equations on graphs to have a clear comparative view. We first formulate a compartmental model to study bifurcations and thresholds mathematically. We later move on with a network-based analysis to illustrate the proliferation of online piracy dynamics with an epidemiological approach over a social network. We figure out a solution for this online piracy problem by developing awareness among individuals and introducing media campaigns, which could be a valuable factor in eradicating and controlling online piracy. Next, using degree-block approximation, network analysis has been performed to investigate the phenomena from a heterogeneous approach and to derive the threshold condition for the persistence of piracy in the population in a steady state. Considering the dual control of positive peer influence and media-driven awareness, we examine the system through realistic parameter selection to better understand the complexity of the dynamics and suggest policy implications.