Optimal Control of Rumor Propagation Model Considering Individual Activity and Platform Effect

In order to accurately predict the spreading trend of rumors and formulate effective control strategies, the rumor spreading model based on the epidemic model is usually used to study the spreading mechanism of rumors. However, the classification of node types in the traditional rumor propagation model is too simple to reflect the characteristics of each node. In this paper, the different attitudes of individuals to rumor spreading are considered, and rumor spreaders are divided into high-activity rumor spreaders and low-activity rumor spreaders. At the same time, due to the platform effect of social network, the situation of spreading rumors through indirect contact such as non-concern/non-friend relationship is considered. On this basis, a S<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">u</inf>S<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">e</inf>I<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</inf>I<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</inf>RW model is established, and the model is optimized by adding reasonable propagation nodes, so as to implement control more accurately and efficiently. In order to reduce the negative impact of rumor spreading at the minimum cost, an optimal control model is established by applying control strategies, and the optimal solution of the rumor spreading model is solved by using Pontryagin minimum principle. Finally, numerical simulation proves that the control strategies proposed in this paper can effectively suppress the spread of rumors at the minimum cost.