Asymptotic Behavior of a Stochastic E-rumor Model with Lévy Jump

Authors

Séverine Bernard University of Antilles, Department of Mathematic and Computer Sciences, LAMIA (EA 4540), BP 250, 97159, Pointe-a-Pitre, Guadeloupe, France
Alain Pietrus University of Antilles, Department of Mathematic and Computer Sciences, LAMIA (EA 4540), BP 250, 97159, Pointe-a-Pitre, Guadeloupe, France
Kendy Valmont University of Antilles, Department of Mathematic and Computer Sciences, LAMIA (EA 4540), BP 250, 97159, Pointe-a-Pitre, Guadeloupe, France

DOI:

https://doi.org/10.37256/cm.132020177

Keywords:

stochastic e-rumor models, Brownian motion, lévy jump, Itô Lévy's formula, extinction, persistence in the mean

Abstract

In this paper, we investigate the effects of a Lévy jump on the dynamic of propagation of a rumor on a social network. The random environment is characterized by white noises and Lévy jump and we establish sufficient conditions for extinction and persistence in the mean of an e-rumor. At the end, we compare our study with our previous one^[7] to see the difference with only white noises.

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Published

2020-06-16

Issue

Contemporary Mathematics, Volume 1 Issue 3 (2020), 112-169

Section

Research Article