Rumors have been widely spread in online social networks and they become a major concern in modern society. This paper is devoted to the design of a cost-effective rumor-containing scheme in online social networks through an optimal control approach. First, a new individual-based rumor spreading model is proposed, and the model considers the influence of the external environment on rumor spreading for the first time. Second, the cost-effectiveness is recommended to balance the loss caused by rumors against the cost of a rumor-containing scheme. On this basis, we reduce the original problem to an optimal control model. Next, we prove that this model is solvable, and we present the optimality system for the model. Finally, we show that the resulting rumor-containing scheme is cost-effective through extensive computer experiments.

中文翻译：

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通过最佳控制方法防御在线社交网络谣言

谣言已在在线社交网络中广泛传播，它们已成为现代社会的主要关注点。本文致力于通过一种最优控制方法，设计一种在线社交网络中具有成本效益的包含谣言的方案。首先，提出了一种新的基于个人的谣言传播模型，该模型首次考虑了外部环境对谣言传播的影响。其次，建议使用成本效益来平衡谣言造成的损失与包含谣言的计划的成本。在此基础上，我们将原始问题简化为最优控制模型。接下来，我们证明该模型是可解的，并且为该模型提供了最优系统。最后，我们通过大量的计算机实验表明，所得的包含谣言的方案具有成本效益。