Advanced Mathematical Models & Applications

The exponential growth of influencer-based social media marketing (SMM) has been paralleled by increasing concerns about its long-term economic viability, specifically return on investment (ROI). While traditional metrics focus on short-term engagement, this study examines the systemic sustainability of SMM through an epidemiological lens. We introduce a Swarm Influence Dynamics (SID) model that formalizes influencer behavior as adaptive particles in a content space, incorporating a digital behavioral pathogen called contentitis, representing compulsive production driven by algorithmic feedback. Our methodology integrates swarm intelligence with compartmental epidemiological modeling to capture the endogenous dynamics of attention economies. Results reveal a critical phase transition: below a threshold Ψ_crit , marketing thrives in a diverse, high-ROI regime; above it, hyper-convergence on trends triggers violent saturation cycles that degrade returns into negative territory. The model demonstrates that SMM's worth follows a non-monotonic trajectory, with platform designs that maximize engagement inadvertently pushing ecosystems toward pathological collapse. We conclude that influencer marketing is only sustainable when platform architectures and marketing strategies actively maintain diversity below the critical threshold, offering design principles for algorithmic moderation and campaign timing that avoid systemic degradation.