Dynamical behaviors and control measures of rumor-spreading model in consideration of the infected media and time delay

Abstract

With the development and the progress of science and technology, the spread of rumors presents new characteristics. The spreaders publish false and malicious rumors on public social networks media, and individuals visit these networks and share them with their friends through the friendship network, which provides a convenient hotbed for the indiscriminate spread of rumors. In this paper, an improved rumor spreading model is established to explore the new characteristics of rumor spreading process on the basis of considering the delay of interactive system. By studying the dynamic behavior of the delay spreading model, we calculate the threshold of rumor spreading extinction, and prove the local and global asymptotic behavior of the boundary equilibrium point and endemic equilibrium point of the model. On this basis, we further consider the control strategies such as deleting rumor posts, popular science education, immunotherapy, etc., and propose an optimal control problem to minimize the spread scale and control cost of rumors. The optimal condition of the optimal control problem is calculated by mathematical analysis, and the correctness of the theoretical results is verified by numerical simulations. Finally, we compare the influence of time delays, optimal control and the media network on rumor spreading.