Dynamic analysis and optimal control of SOIMR rumor propagation model considering the effect of media reports and time delay

Media reports and opposite factors have an important impact on the spread of rumors. When rumors appear on social networks, the media in the relevant departments need time to react before they can make authoritative announcements. The effects of media coverage and time lag on the spread of rumors, as well as the impact of individual rebuttals on the spread of rumors, are considered. This paper proposes a SOIMR (Susceptibility-Opposite-Infection-Media-Remover) model with media coverage and time lag. Firstly, the basic regeneration number and the equilibrium point of the model are obtained. Then, the local asymptotic stability of the equilibrium point of the model is demonstrated. On this basis, the control strategy is further considered, and the optimal control problem of maximizing the scale and control cost of rumor propagation is proposed. Finally, the accuracy of the theoretical results and the influence of different parameters of the model are verified by numerical simulations, the greater the number of rumor opponents, the shorter the time lag of media reports, the greater the influence of media reports, and the more effective the suppression of rumors.