Stability Analysis of a New E-rumor Model

Séverine Bernard (), Ténissia Cesar () and Alain Pietrus ()
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Séverine Bernard: Université des Antilles
Ténissia Cesar: Université des Antilles
Alain Pietrus: Université des Antilles

A chapter in Control Systems and Mathematical Methods in Economics, 2018, pp 377-390 from Springer

Abstract: Abstract The emergence of new communication tools leads us to have public discussions on social networks. These public spaces of exchange are firmly established in our societies but are strong sensors of both human behaviors and collective feelings. The propagation of rumors, namely e-rumor, is very fast and is one of the most dangerous for a society because it can destabilize financial, political and economical markets. Many mathematical models, based on the epidemic ones, have been constructed in order to understand this multi-dimensional diffusion process driven mainly by socio-psychological elements. In this paper, we propose a new model of propagation of rumor taking into account the different possible changes of classes of the individuals of a social network. With this new model, we point out admissible equilibrium states and the conditions of their stability, as well as the criteria of persistence of this model.

Date: 2018
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DOI: 10.1007/978-3-319-75169-6_18

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