| Abstract: |
| \noindent In recent years, social networks became new spaces of discussions which can be dangerous for our societies because it can destabilize human behaviors and collective feelings. Namely e-rumor, the propagation of informations on social networks is a multi-dimensional diffusion process mainly driven by socio-psychological and geographical elements.\
\noindent The first e-rumor models are based on the epidemic ones and some control studies of fakes news have been made for deterministic ones. Then a stability analysis has been done on a new model better taking into account the dynamic within the social network. But this phenomenom is a random one and the use of stochastic models proved useful. \
\noindent From a deterministic e-rumor model, we first propose a stochastic one with only white noises. But e-rumor systems can suffer social perturbations such as election period, social movement, etc. Such events can be described by L\`evy jump process. Consequently, we propose then a stochastic e-rumor model with jumps, for which we give the extinction and persistence thresholds of an information on a social network. |
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