An improved ISR-WV rumor propagation model based on multichannels with time delay and pulse vaccination

The rapid development of the Internet has broadened the channels of dissemination of information, it has also led to the rapid and widespread propagation of rumors, which can have a serious negative impact socially. In this paper, an improved ISR-WV rumor propagation model integrating multichannels is proposed by considering the system’s time delay, and the influence of different channels of propagation on the dynamic process is further analyzed. Moreover, the basic reproduction number R₀, rumor-free equilibrium, and rumor-prevailing equilibrium, as well as their stability, are deduced. Then, an optimal control problem with pulse vaccination is designed. Finally, the validity of the model and theoretical results is verified by numerical simulations and a practical application. The results show that the rumor propagation threshold R₀ is more sensitive to the rate of the propagation of the information base channel. The shorter the thinking time τ₁ required for the ignorant to react after obtaining the information, the larger the final scale of propagation. Under this condition, the time delay τ₂ spent by a spreader in producing a video is negatively related to the final scale of the propagation; conversely, a longer τ₁ implies that the person tends to more cognizant, which can suppress the spread of rumors. Under this condition, τ₂ has little effect on the final scale of propagation. In addition, the results also prove that timely implementation of the pulse vaccination control strategy of popular science education can effectively control the propagation of rumors and reduce their negative impact.