A model of an online social network (OSN)

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Abstract

We introduce a new epidemic framework to model the adoption and abandonment dynamics of users on an online social network (OSN), with special emphasis on the novel compartment pauci-engaged. Pauci-engaged individuals have been exposed to an invitation to an OSN, but remain undecided about joining, thus reflecting real-world hesitation and trial behaviors. Building on the infectious–recovery dynamics studied by Chen, Kong, and Wang, we derive the basic reproduction number R₀ and establish threshold conditions for the stability of both the user-free equilibrium and the user-prevailing equilibrium. Local stability analysis using the Jacobian matrix, together with global stability results based on Lyapunov functions, shows that when the basic reproduction number R₀ < 1, the OSN cannot sustain an engaged user base, while when R₀ > 1, a persistent engagement state emerges. Our findings highlight the pivotal role of the decision-making phase in the growth of the digital platform and offer actionable insights to optimize user recruitment and retention strategies in OSNs.

Keywords

online social network / equilibrium / stability analysis

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