International Journal of Mathematical Sciences and Computing (IJMSC)
IJMSC Vol. 11, No. 3, 8 Oct. 2025
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SIP Model and Bifurcation Analysis for Spread of Misinformation in Online Social Networks
PDF (494KB), PP.19-31
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Author(s)
Nitesh Narayan
1
Kaushik Haldar
2,*
Index Terms
SIP Model, Bifurcation, Stability, Numerical Simulation, Misinformation, Social Network
Abstract
The spreading of misinformation in Online Social Networks (OSNs) is quite similar to the spreading of infection in biological diseases. As the biological virus spreads and makes one infected as well as those who come into contact with the infected person, the nature and behavior of the spread of misinformation in an online social network is similar. So in order to understand the functioning of misinformation and to control over epidemic outbreak of misinformation in OSNs, epidemic models can be quite handy. The introduction of Bifurcation theory in the epidemic model explains the qualitative behavior of the system with changes in parameters. In this paper, we have introduced the Susceptible, Infectious, and Protected (SIP) model with Bifurcation for the propagation of misinformation in OSNs. Here Bifurcation is due to the limited number of users who are ready to adopt the Security and Privacy Policies of Social Network Sites. We define the threshold number for the system of equations and explain the stability of an Infection Free Equilibrium (IFE), representing the absence of misinformation. We have discussed about the endemic equilibrium point and bifurcation conditions along with its nature and stability at those points. Also, we have shown global stability at the endemic Equilibrium of the system. Finally, numerical simulation has been used to show the existence of bifurcation in the system with a change in the value of parameters.
Cite This Paper
Nitesh Narayan, Kaushik Haldar, "SIP Model and Bifurcation Analysis for Spread of Misinformation in Online Social Networks", International Journal of Mathematical Sciences and Computing(IJMSC), Vol.11, No.3, pp. 19-31, 2025. DOI: 10.5815/ijmsc.2025.03.02
Reference
[1]Cruz Vargas-De-Leon, On the global stability of SIS,SIR and SIRS epidemic models with standard incidence, Chaos, Solitons & Fractals Nonlinear Science, and Non-equilibrium and Complex Phenomena, 44(2011) 1106-1110.
[2]Kermack, W. O. and McKendrick, A. G., A contribution to the mathematical theory of epidemics, Proceedings of the Royal Society A, 115, 700–721, 1927.
[3]John Cannarella, Joshua A. Spechler, Epidemiological modeling of online social network dynamics, http://arxiv.org/abs/1401.4208v1.
[4]Lett E., “Understanding Social Network site users’ privacy tool use”, Computer in Human Behaviour 29(2013) 1649-1656.
[5]LI, Yan; Yingjiu LI; YAN, Qiang; and DENG, Robert H. Privacy leakage analysis in online social networks. (2015). Computers and Security. 49, 239-254. Research Collection School Of Information Systems.
[6]Wendi Wang, Shigui Raun, Bifurcation in Epidemic Moel with constant removal rate of the infectives, Journal of Mathematical Analysis and Application,291(2004) 775-793.
[7]Xiang Zhu, Yuanping Nie, and Aiping Li, Demographic Prediction of Online Social Network Based on Epidemic Model, APWeb 2014 Workshops, LNCS 8710, pp. 93–103, 2014.
[8]Zhaoyang Zhang, Honggang Wang, Chonggang Wang and Hua Fang, Modeling Epidemics Spreading on Social Contact Networks, IEEE Transactions on Emerging topics in Computing, Volume 3, No. 3, September 2015.
[9]2016 West Bengal Legislative Assembly election, at https://en.wikipedia.org/wiki/2016_West_Bengal_Legislative_Assembly_election.
[10]Data check: 45 million new, young voters could play a key role in 2019 elections, at https://scroll.in/article/913411/data-check-45-million-new-young-voters-could-play-a-key-role-in-2019-elections.
[11]Distribution of Twitter users worldwide as of January 2021, by age group,at https://www.statista.com/statistics/283119/age-distribution-of-global-twitter-users/.
[12]Hawksey, M.: Twitter Archiving Google Spreadsheet TAGS v6.1. JISC CETIS MASHe: The Musing of Martin Hawksey (EdTech Explorer) (2013), https://docs.google.com/spreadsheets/d/1H8lN1Y13MOhgTHc_lt7-sGyy9JWf-MeEeKzb7eH7s-M/copy.