Bernard, Séverine; Bouza, Gemayqzel; Piétrus, Alain An optimal control approach for e-rumor. (English) Zbl 1473.49024 Rev. Invest. Oper. 36, No. 2, 108-114 (2015). Summary: Social networks have a significant role in spreading rumors. Such phenomena of e-rumor are big challenges for communities, organizations and states, since the spread of rumors can rapidly jeopardise their public opinion and their economic and financial markets. In these last decades, many mathematical theories have been developed on this topic both in algebraic and numerical terms. In the present work, an optimal control approach is applied on a rumor’s dynamical model in order to minimize the spread. At the end of the paper some numerical results are given. Cited in 4 Documents MSC: 49K15 Optimality conditions for problems involving ordinary differential equations 49S05 Variational principles of physics 94A15 Information theory (general) 91D30 Social networks; opinion dynamics Keywords:social networks; e-rumor; optimal control; Cauchy-Lipschitz’s theorem; Pontryagin’s maximum principle PDFBibTeX XMLCite \textit{S. Bernard} et al., Rev. Invest. Oper. 36, No. 2, 108--114 (2015; Zbl 1473.49024) Full Text: Link References: [1] DALEY D.J. and D.G. KENDALL (1964): Epidemics and rumours, Nature 204, 11-18. [2] DALEY D.J. and D.G. KENDALL (1965): Stochastic rumours, IMA J. of Applied Mathematics 1, 42-55. [3] HUANG J. and X. JIN (2011): Preventing rumor spreading on small-world networks, J. Syst. Sci. Complex 24, 449-456. [4] LAARABI H., E. H. LABRIJI, M. RACHIK and A. KADDAR (2012): Optimal control of an epidemic model with a saturated incidence rate, Nonlinear Analysis: Modelling and control, 17, 448-459. · Zbl 1290.49004 [5] LEDZEWICZ U. and H. SCHATTLER (2011): On optimal singular controls for a general SIR-model with vaccination and treatment, Discrete and Continuous Dynamical Systems, Supplement 981-990. · Zbl 1306.49056 [6] D. Maki (1973): Mathematical models and applications, with emphasis on social, life, and management sciences, Englewood Cliffs, New Jersey, Prentice Hall College Div. [7] PONTRYAGIN L. , V. BOLTYANSKI, R. GAMKRELIDZE and E. MICHTCHENKO (1974): Théorie mathématique des processus optimaux, Editions Mir, Moscou. · Zbl 0289.49002 [8] STATTNER E., M. COLLARD and N. VIDOT (2011): Diffusion in dynamic social networks: applica-tions in epidemiology. In Database and Expert Systems Applications, 559-573. Springer, Berlin. [9] TRÉLAT E.(2008): Contrôle optimal: théorie et applications, Vuibert This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.