Dynamic analysis and control strategies of the SEIHR rumor diffusion model in online social networks

With the prevalence of online social networks, rumors spread rampantly online. The versatility and complexity of human attitudes make dissemination more challenging to portray, so it is meaningful to develop a more comprehensive diffusion model. To this end, an improved SEIHR model considering three attitudes towards rumors is proposed. Then we deduce the stability of the dynamics model and use two scenarios to validate its accuracy. Meanwhile, rumor diffusion generates extensive social threats. To mitigate such threats, we introduce three immunization strategies and forge bonds among their basic reproduction numbers. Besides, we develop three synergistic optimal controls that vary with the time and degree to impede rumor diffusion. The analysis of the optimal control problem is conducted by Pontryagin's maximum principle. Next, experiments are conducted to verify the efficacy of the SEIHR model and control strategies. Our simulations show that adding the exposed and the hibernated undermines the impact of rumors and puts off terminal time. Additionally, immunization strategies effectively curb rumor diffusion. Moreover, the combination of three synergistic optimal controls leads to the smallest rumor scale and the least cumulative total costs.