In this research, we propose and study an online social network mathematical model with delay based on two innovative assumptions: (1) newcomers are entering community as either potential online network users or that who are never interested in online network at constant rates, respectively; and (2) it takes a certain time for the active online network users to start abandoning the network. The basic reproduction R₀, the user-free equilibrium(UFE) P₀, and the user-prevailing equilibrium(UPE) P^* are identified. The analysis of local and global stability for those equilibria is carried out. For the UPE P^*, using the delay τ as the Hopf bifurcation parameter, the occurrence of Hopf bifurcation is investigated. The conditions are established that guarantee the Hopf bifurcation occurs as τ crosses the critical values. Numerical simulations are provided to illustrate the theoretical results.
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Wang et al. (2023) studied this question.
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