Stability and optimal control for delayed rumor-spreading model with nonlinear incidence over heterogeneous networks
Xupeng Luo(罗续鹏)1,2, Haijun Jiang(蒋海军)1,†, Shanshan Chen(陈珊珊)1, and Jiarong Li(李佳容)1
1 College of Mathematics and System Sciences, Xinjiang University, Urumqi 830017, China; 2 College of Mathematics and Physics, Guangxi Minzu University, Nanning 530006, China
Abstract On the multilingual online social networks of global information sharing, the wanton spread of rumors has an enormous negative impact on people's lives. Thus, it is essential to explore the rumor-spreading rules in multilingual environment and formulate corresponding control strategies to reduce the harm caused by rumor propagation. In this paper, considering the multilingual environment and intervention mechanism in the rumor-spreading process, an improved ignorants-spreaders-1-spreaders-2-removers (I2SR) rumor-spreading model with time delay and the nonlinear incidence is established in heterogeneous networks. Firstly, based on the mean-field equations corresponding to the model, the basic reproduction number is derived to ensure the existence of rumor-spreading equilibrium. Secondly, by applying Lyapunov stability theory and graph theory, the global stability of rumor-spreading equilibrium is analyzed in detail. In particular, aiming at the lowest control cost, the optimal control scheme is designed to optimize the intervention mechanism, and the optimal control conditions are derived using the Pontryagin's minimum principle. Finally, some illustrative examples are provided to verify the effectiveness of the theoretical results. The results show that optimizing the intervention mechanism can effectively reduce the densities of spreaders-1 and spreaders-2 within the expected time, which provides guiding insights for public opinion managers to control rumors.
Fund: Project supported by the National Natural Science Foundation of People's Republic of China (Grant Nos. U1703262 and 62163035), the Special Project for Local Science and Technology Development Guided by the Central Government (Grant No. ZYYD2022A05), and Xinjiang Key Laboratory of Applied Mathematics (Grant No. XJDX1401).
Xupeng Luo(罗续鹏), Haijun Jiang(蒋海军), Shanshan Chen(陈珊珊), and Jiarong Li(李佳容) Stability and optimal control for delayed rumor-spreading model with nonlinear incidence over heterogeneous networks 2023 Chin. Phys. B 32 058702
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