Abstract
In this paper, we consider a population of a social network in which a fake news propagates and divides it into four categories: ignorants, spreaders, stiflers who accept the rumor, and stiflers who oppose the rumor. Starting from a SIR type model describing the propagation of e-rumor, we modify it by adding some external actions and control them in order to reduce the spread of a bad information. To carry out this investigation, we use known facts from optimal control theory. Numerical simulations illustrate the efficiency of the obtained control strategy.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Albi, G., Pareschi, L., Toscani, G., Zanella, M.: Recent advances in opinion modeling: control and social influence. In: Bellomo, N., Degond, P., Tadmor, E. (eds.) Active Particles, Volume 1. MSSET, pp. 49–98. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-49996-3_2
Bernard, S., Bouza, G., Piétrus, A.: An optimal control approach for e-rumor. Revista Investigación Operacional 36(2), 108–114 (2015)
Bernard, S., Bouza, G., Piétrus, A.: An e-rumour model with control on the spreaders. Comptes rendus de l’Académie Bulgare des Sciences 69(11), 1407–1414 (2016)
Bernard, S., Cesar, A.T.: Piétrus, Some actions to control e-rumor. e-J. Carib. Acad. Sci. 9(1) (2017)
Daley, D.J., Kendall, D.G.: Epidemics and rumors. Nature 204, 11–18 (1964)
Daley, D.J., Kendall, D.G.: Stochastic rumors. IMA J. Appl. Math. 1, 42–55 (1965)
Hansen, E., Day, T.: Optimal control of epidemics with limited resources. J. Math. Biol. 62, 423–451 (2011)
Huang, J., Jin, X.: Preventing rumor spreading on small-world networks. J. Syst. Sci. Complex 24, 449–456 (2011)
Ledzewicz, U., Schattler, H.: On optimal singular controls for a general SIR-model with vaccination and treatment. Discrete Continuous Dyn. Syst. Ser. B, (Suppl.), 981–990 (2011)
Liu, J., Niu, K., He, Z., Lin, J.: Analysis of rumor spreading in communities based on modified SIR model in microblog. In: Agre, G., Hitzler, P., Krisnadhi, A.A., Kuznetsov, S.O. (eds.) AIMSA 2014. LNCS (LNAI), vol. 8722, pp. 69–79. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-10554-3_7
Maki, D.: Mathematical Models and Applications, with Emphasis on Social, Life and Management Sciences. Prentice Hall College Div, Englewood Cliffs (1973)
Pontryaguin, L., Boltyanski, V., Gamkrelidze, R., Michtchenko, E.: Théorie mathématique des processus optimaux. Editions Mir, Moscou (1974)
Trélat, E.: Contrôle optimal: théorie et applications. Vuibert, Paris (2008)
Zanette, D.H.: Dynamics of rumor propagation on small-world networks. Phys. Rev. E 65, 041908 (2002)
Acknowledgment
The authors would like to thank Mr. Raphael Pasquier, of the C3I center of the University of “Antilles”, who helped us to perform the different figures. We also thank the anonymous referees for their valuable remarks and comments which improved the presentation of this manuscript.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG
About this paper
Cite this paper
Bernard, S., César, T., Piétrus, A. (2018). Spreading Rumors and External Actions. In: Lirkov, I., Margenov, S. (eds) Large-Scale Scientific Computing. LSSC 2017. Lecture Notes in Computer Science(), vol 10665. Springer, Cham. https://doi.org/10.1007/978-3-319-73441-5_20
Download citation
DOI: https://doi.org/10.1007/978-3-319-73441-5_20
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-73440-8
Online ISBN: 978-3-319-73441-5
eBook Packages: Computer ScienceComputer Science (R0)