The stochastic evolution of a rumor spreading model with two distinct spread inhibiting and attitude adjusting mechanisms in a homogeneous social network

Ming Li; Hong Zhang; Paul Georgescu; Tan Li

doi:10.1016/j.physa.2020.125321

The stochastic evolution of a rumor spreading model with two distinct spread inhibiting and attitude adjusting mechanisms in a homogeneous social network

Physica A. 2021 Jan 15:562:125321. doi: 10.1016/j.physa.2020.125321. Epub 2020 Sep 29.

Authors

Ming Li¹, Hong Zhang¹, Paul Georgescu², Tan Li³

Affiliations

¹ School of Economics and Management, Changzhou Institute of Technology, Changzhou, Jiangsu 213032, PR China.
² Department of Mathematics, Technical University of Iaşi, Bd. Copou 11A, 700506 Iaşi, Romania.
³ School of Innovation and Entrepreneurship, Changzhou Institute of Technology, Changzhou, Jiangsu 213032, PR China.

Abstract

In this paper, we propose and analyze from a stability viewpoint a deterministic, ODE-based class of rumor spreading models with two distinct inhibiting and adjusting mechanisms, together with its corresponding stochastic counterpart. For the deterministic model, a threshold parameter $R_{0}$ defined ad hoc, called the basic influence number, is used to ascertain whether the rumors are prevailing or not. If $R_{0} < 1$ , the rumor-free equilibrium is found to be locally asymptotically stable, while if $R_{0} > 1$ it is shown that there is at least one additional rumor-prevailing equilibrium, which is necessarily locally asymptotically stable. For the stochastic model, we first show that there exists a unique global solution. Subsequently, we investigate the asymptotic behavior of the stochastic system around the equilibria of the deterministic system by constructing suitable Lyapunov functionals. Furthermore, numerical simulations are given to illustrate, support and enhance our theoretical analysis.

Keywords: Basic influence number; Deterministic model; Inhibiting and adjusting mechanisms; Rumor spreading; Stochastic model.