Affiliation:
1. Department of Mathematics, College of Science, King Saud University, P.O. Box 1142, Riyadh 11989, Saudi Arabia
2. Department of Mathematics, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia
Abstract
Sensitively altered news, commonly referred to as rumors, can lead an individual, organization, or nation astray, potentially resulting in harm, even to the extent of causing violence among large groups of people. In this digital age, news can be easily twisted and rapidly spread through the internet and social media. It becomes challenging for consumers to discern whether the information they encounter online has been manipulated. Unfortunately, the rise of internet forgeries has facilitated the dissemination of false or distorted information by unscrupulous individuals, particularly on sensitive matters, to serve their own interests. Once a rumor is generated and made public on the internet, it quickly spreads through sharing and discussions by anonymous individuals, sometimes intentionally, without thorough fact-checking. In this manuscript, we investigate the dynamical model of rumor propagation in a social network using the classical Caputo piecewise derivative. We examine the existence and uniqueness of a solution for the aforementioned problem and analyze the equilibrium, stability, boundedness, and positivity of the model. To obtain the numerical simulation of the piecewise derivative, we employ various fractional orders, and the approximate solution of the considered model is found using the fractional piecewise numerical iterative approach of the Newton polynomial. This approach allows us to gain valuable insights into the dynamics of rumor propagation and its effects within a social network.
Subject
Physics and Astronomy (miscellaneous),General Mathematics,Chemistry (miscellaneous),Computer Science (miscellaneous)
Reference35 articles.
1. Allport, G.W., and Postman, L. (1947). The Psychology of Rumor, Holt Rinehart and Winston.
2. Bordia, P., and Difonzo, N. (2005). Psychological motivations in rumor spread. Anal. Commer. Rumors Perspect. Mark. Manag. Rumor Preval. Eff. Control Tactics, 87–101.
3. On the control of a reaction-diffusion system: A class of SIR distributed parameter systems;Ghazzali;Int. J. Dyn. Control,2019
4. (2020, April 01). Available online: https://zephoria.com/top-15-valuable-facebook-statistics/.
5. Epidemics and rumors;Daley;Nature,1964