Studying the Dynamics of the Rumor Spread Model with Fractional Piecewise Derivative

被引:1
|
作者
Alkahtani, Badr Saad T. [1 ]
Alzaid, Sara Salem [2 ]
机构
[1] King Saud Univ, Coll Sci, Dept Math, POB 1142, Riyadh 11989, Saudi Arabia
[2] King Saud Univ, Dept Math, POB 2455, Riyadh 11451, Saudi Arabia
来源
SYMMETRY-BASEL | 2023年 / 15卷 / 08期
关键词
rumor spread model; piecewise derivative; classical derivative; Caputo operator; MATHEMATICAL-MODEL; TRANSMISSION;
D O I
10.3390/sym15081537
中图分类号
O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];
学科分类号
07 ; 0710 ; 09 ;
摘要
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.
引用
收藏
页数:16
相关论文
共 50 条
  • [1] A NUMERICAL STUDY ON THE DYNAMICS OF DENGUE DISEASE MODEL WITH FRACTIONAL PIECEWISE DERIVATIVE
    Khan, Javed
    Rahman, Mati Ur
    Riaz, Muhammad Bilal
    Awrejcewicz, Jan
    FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY, 2022, 30 (08)
  • [2] Modeling Ebola Dynamics with a Φ-Piecewise Hybrid Fractional Derivative Approach
    Alraqad, Tariq
    Almalahi, Mohammed A.
    Mohammed, Naglaa
    Alahmade, Ayman
    Aldwoah, Khaled A.
    Saber, Hicham
    FRACTAL AND FRACTIONAL, 2024, 8 (10)
  • [3] Rumor spread dynamics and its sensitivity analysis under the influence of the Caputo fractional derivatives
    Baishya, Chandrali
    Naik, Manisha Krishna
    Premakumari, R. N.
    COMPUTATIONAL METHODS FOR DIFFERENTIAL EQUATIONS, 2024, 12 (02): : 236 - 265
  • [4] Piecewise mABC fractional derivative with an application
    Khan, Hasib
    Alzabut, Jehad
    Gomez-Aguilar, J. F.
    Agarwal, Praveen
    AIMS MATHEMATICS, 2023, 8 (10): : 24345 - 24366
  • [5] A FRACTIONAL ORDER MODEL FOR THE DYNAMICS OF TUBERCULOSIS SPREAD
    Muhafzan
    Narwen
    Zulakmal
    Baqi, Ahmad iqbal
    COMMUNICATIONS IN MATHEMATICAL BIOLOGY AND NEUROSCIENCE, 2025,
  • [6] The impact of official rumor-refutation information on the dynamics of rumor spread
    Zhang, Yi
    Xu, Jiuping
    Nekovee, Maziar
    Li, Zongmin
    PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, 2022, 607
  • [7] A numerical study of dengue internal transmission model with fractional piecewise derivative
    Ahmad, Shabir
    Yassen, Mansour F.
    Alam, Mohammad Mahtab
    Alkhati, Soliman
    Jarad, Fahd
    Riaz, Muhammad Bilal
    RESULTS IN PHYSICS, 2022, 39
  • [8] A Kinetic Model for the Spread of Rumor in Emergencies
    Chen, Guanghua
    Shen, Huizhang
    Ye, Teng
    Chen, Guangming
    Kerr, Naphtali
    DISCRETE DYNAMICS IN NATURE AND SOCIETY, 2013, 2013
  • [9] Stochastic covid-19 model with fractional global and classical piecewise derivative
    Jain, Sonal
    El-Khatib, Youssef
    RESULTS IN PHYSICS, 2021, 30
  • [10] A MATHEMATICAL MODEL FOR NIPAH VIRUS DISEASE BY USING PIECEWISE FRACTIONAL ORDER CAPUTO DERIVATIVE
    Shah, Kamal
    Khan, Aziz
    Abdalla, Bahaaeldin
    Abdeljawad, Thabet
    Khan, Khalid Ali
    Fractals, 2024, 32 (02):