Top

Journal of Applied Mathematics and Computing

Published in:

01-11-2021 | Original Research

Dynamics and control of delayed rumor propagation through social networks

Authors: Moumita Ghosh, Samhita Das, Pritha Das

Published in: Journal of Applied Mathematics and Computing | Issue 5/2022

Activate our intelligent search to find suitable subject content or patents.

search-config

AI-assisted search

Off

Abstract

Investigation of rumor spread dynamics and its control in social networking sites (SNS) has become important as it may cause some serious negative effects on our society. Here we aim to study the rumor spread mechanism and the influential factors using epidemic like model. We have divided the total population into three groups, namely, ignorant, spreader and aware. We have used delay differential equations to describe the dynamics of rumor spread process and studied the stability of the steady-state solutions using the threshold value of influence which is analogous to the basic reproduction number in disease model. Global stability of rumor prevailing state has been proved by using Lyapunov function. An optimal control system is set up using media awareness campaign to minimize the spreader population and the corresponding cost. Hopf bifurcation analyses with respect to time delay and the transmission rate of rumors are discussed here both analytically and numerically. Moreover, we have derived the stability region of the system corresponding to change of transmission rate and delay values.

previous article Numerical solutions of inverse time fractional coupled Burgers’ equations by the Chebyshev wavelet method

next article On sufficiency and duality theorems for nonsmooth semi-infinite mathematical programming problem with equilibrium constraints

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 340 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

inform now

Edosomwan, Simeon, Prakasan, S.K., Kouame, D., Watson, J., Seymour, T.: The history of social media and its impact on business. J. Appl. Manag. Entrepreneurship 16, 79–91 (2011)

Itani, O., Agnihotri, R., Dingus, R.: Social media use in b2b sales and its impact on competitive intelligence collection and adaptive selling: examining the role of learning orientation as an enabler Ind. Market. Manag. 66, 64–79 (2017)

Hill, E.M., Griffiths, F.E., House, T.: Spreading of healthy mood in adolescent social networks. Proc. R. Soc. B Biol. Sci. 282(1813), 20151180 (2015)CrossRef

Koetsier, J.: Why 2020 is a critical global tipping point for social media Frobes, Dated Feb 18, (2020)

Zubiaga, A., Liakata, M., Procter, R., Bontcheva, K., Tolmie, P.: Towards detecting rumours in social media. In: Association for the Advancement of Artificial Intelligence Workshop, 04 (2015)

Scatà, M., Di Stefano, A., La Corte, A., & Liò, P.: Quantifying the propagation of distress and mental disorders in social networks Sci. Rep. 8(1), 1–12 (2018)

Qiu, X., Zhao, L., Wang, J., Wang, X., Wang, Q.: Effects of time-dependent diffusion behaviors on the rumor spreading in social networks. Phys. Lett. A 380(24), 2054–2063 (2016)MathSciNetCrossRef

Centola, D.: The spread of behavior in an online social network experiment. Science 329(5996), 1194–1197 (2010)CrossRef

Coronavirus: Chicken prices fall, poultry industry affected. The Economic Times News, Accessed on March 09, (2020)

10.

U.S. Securities and Exchange Commission. SEC charges: False tweets sent two stocks reeling in market manipulation. Accessed on Nov. 5, (2020). https://www.sec.gov/news/pressrelease/2015-254.html

11.

Zhang, P., Bao, Z., Niu, Y., Zhang, Y., Mo, S., Geng, F., Peng, Z.: Proactive rumor control in online networks. World Wide Web 22(4), 1799–1818 (2019)CrossRef

12.

Moreno, Y., Nekovee, M., Pacheco, A.F.: Dynamics of rumor spreading in complex networks. Phys. Rev. E 69, 066130 (2004)CrossRef

13.

Kawachi, K.: Deterministic models for rumor transmission. Nonlinear Anal. Real World Appl. 9(5), 1989–2028 (2008)MathSciNetMATHCrossRef

14.

Das, S., Das, P., Das, P.: Control of nipah virus outbreak in commercial pig-farm with biosecurity and culling Math. Model. Nat. Phenom. 15, 64 (2020)

15.

Das, S., Das, P., Das, P.: Chemical and biological control of parasite-borne disease Schistosomiasis: An impulsive optimal control approach. Nonlinear Dynamics 104(1), 603–628 (2021)

16.

Das, S., Das, P., Das, P.: Optimal control of behaviour and treatment in a nonautonomous SIR model. Int. J. Dyn. Syst. Differ. Equ. 11(2), 108–130 (2021)MathSciNetMATH

17.

Das, P., Nadim, S. S., Das, S., Das, P.: Dynamics of covid-19 transmission with comorbidity: a data driven modelling based approach. Nonlinear Dynamics 1–15 (2021)

18.

Kuniya, T., Bentout, S., Chekroun, A.: Parameter estimation and prediction for coronavirus disease outbreak 2019 (COVID-19) in algeria. AIMS Public Health 7(2), 306–318 (2020)CrossRef

19.

Yosyingyong, P., Viriyapong, R.: Global stability and optimal control for a hepatitis B virus infection model with immune response and drug therapy. J. Appl. Math. Comput. 60(1), 537–565 (2019)MathSciNetMATHCrossRef

20.

Soufiane, B., Touaoula, T.M.: Global analysis of an infection age model with a class of nonlinear incidence rates. J. Math. Anal. Appl. 434(2), 1211–1239 (2016)MathSciNetMATHCrossRef

21.

Bentout, S., Chen, Y., Djilali, S.: Global dynamics of an SEIR model with two age structures and a nonlinear incidence. Acta Applicandae Mathematicae 171(1), 7 (2020)MathSciNetMATHCrossRef

22.

Bentout, S., Tridane, A., Djilali, S., Touaoula, T.M.: Age-structured modeling of covid-19 epidemic in the USA, UAE and Algeria. Alexandria Eng. J. 60(1), 401–411 (2021)CrossRef

23.

Bentout, S., Kumar, S., Djilali, S.: Hopf bifurcation analysis in an age-structured heroin model. Eur. Phys. J. Plus 136(2), 260 (2021)CrossRef

24.

Bentout, S., Djilali, S., Chekroun, A.: Global threshold dynamics of an age structured alcoholism model. Int. J. Biomath. 14(03), 2150013 (2021)MathSciNetMATHCrossRef

25.

Djilali, S., Bentout, S.: Spatiotemporal patterns in a diffusive predator-prey model with prey social behavior. Acta Applicandae Mathematicae 169(1), 125–143 (2020)MathSciNetMATHCrossRef

26.

Ghanbari, B., Djilali, S.: Mathematical and numerical analysis of a three-species predator-prey model with herd behavior and time fractional-order derivative. Math. Methods Appl. Sci. 43, 1736–1752 (2020)MathSciNetMATHCrossRef

27.

Souna, F., Djilali, S., Charif, F.: Mathematical analysis of a diffusive predator-prey model with herd behavior and prey escaping. Math. Model. Nat. Phenom. 15, 23 (2020)MathSciNetMATHCrossRef

28.

Djilali, S.: Pattern formation of a diffusive predator-prey model with herd behavior and nonlocal prey competition. Math. Methods Appl. Sci. 43(5), 2233–2250 (2020)MathSciNetMATHCrossRef

29.

Daley, D.J., Kendall, D.G.: Epidemics and rumours. Nature 204(4963), 1118–1118 (1964)CrossRef

30.

Wang, J., Zhao, L., Huang, R.: 2SI2R rumor spreading model in homogeneous networks. Physica A Stat. Mech. Appl. 413, 153–161 (2014)MathSciNetMATHCrossRef

31.

Hu, Y., Pan, Q., Hou, W., He, M.: Rumor spreading model with the different attitudes towards rumors. Physica A Stat. Mech. Appl. 502, 331–344 (2018)MathSciNetMATHCrossRef

32.

Dhar, J., Jain, A., Gupta, V.: A mathematical model of news propagation on online social network and a control strategy for rumor spreading. Soc. Netw. Anal. Min. 6, 57 (2016)CrossRef

33.

Jain, A., Dhar, J., Gupta, V.: Stochastic model of rumor propagation dynamics on homogeneous social network with expert interaction and fluctuations in contact transmissions. Physica A Stat. Mech. Appl. 519, 227–236 (2019)MathSciNetMATHCrossRef

34.

Zhu, L., Liu, M., Li, Y.: The dynamics analysis of a rumor propagation model in online social networks. Physica A Stat. Mech. Appl. 520, 118–137 (2019)MathSciNetMATHCrossRef

35.

Jain, A., Dhar, J., Gupta, V.K.: Optimal control of rumor spreading model on homogeneous social network with consideration of influence delay of thinkers. Differ. Equ. Dyn. Syst. 1–22, (2019)

36.

Huo, L., Lin, T., Fan, C., Liu, C., Zhao, J.: Optimal control of a rumor propagation model with latent period in emergency event. Adv. Differ. Equ. 2015(1), 54 (2015)MathSciNetMATHCrossRef

37.

Misra, A.K., Sharma, A., Shukla, J.B.: Modeling and analysis of effects of awareness programs by media on the spread of infectious diseases. Math. Computer Model. 53(5), 1221–1228 (2011)MathSciNetMATHCrossRef

38.

Misra, A.K., Sharma, A., Singh, V.: Effect of awareness programs in controlling the prevalence of an epidemic with time delay. J. Biol. Syst. 19(02), 389–402 (2011)MathSciNetMATHCrossRef

39.

Li, T., Guo, Y.: Optimal control of an online game addiction model with positive and negative media reports. J. Appl. Math., Comput (2020)MATH

40.

BBC News:. AP twitter account hacked in fake ‘white house blasts’ post. Accessed on 2016-02-25

41.

Pontryagin, L.S.: Mathematical Theory of Optimal Processes. CRC Press, USA (1962)

42.

Zubiaga, A., Liakata, M., Procter, R., Wong Sak Hoi, G., Tolmie, P.: Analysing how people orient to and spread rumours in social media by looking at conversational threads. PLoS ONE. 11(3), e0150989 (2016)CrossRef

43.

Driessche, P., Watmough, J.: Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. Math. Biosci. 180, 29–48 (2002)MathSciNetMATHCrossRef

44.

Times, Hindustan, Jeelani, G.: RBI says Rs 10 coin is valid, those refusing to accept may face legal action. Accessed on Sept. (2016)

45.

Roy, P.K., Saha, S., Al Basir, F.: Effect of awareness programs in controlling the disease HIV/AIDS: an optimal control theoretic approach. Adv. Differ. Equ. 2015(1), 217 (2015)MathSciNetMATHCrossRef

46.

Zaman, G., Kang, Y.H., Jung, H.: Stability analysis and optimal vaccination of an SIR epidemic model. Biosystems 93(3), 240–249 (2008)CrossRef

47.

Fleming, W.H., Rishel, R.W.: Deterministic and stochastic optimal control. Springer, Applications of mathematics (1975)

48.

Ruan, S., Wei, J.: On the zeros of transcendental functions with applications to stability of delay differential equations with two delays. Dyn. Contin. Discret. Impuls. Syst. Series A Math. Anal. 10(6), 863–874 (2003)MathSciNetMATH

49.

Jamieson, K.H.: Cyberwar: How Russian Hackers and Trolls Helped Elect a President What We Don’t, Can’t, and Do Know. Oxford University Press, Oxford (2018)

50.

Kelly Garrett, R.: Social media’s contribution to political misperceptions in u.s. presidential elections. PLoS ONE, 14(3), e0213500, (2019)

51.

Lenhart, S., Workman, J.T.: Optimal Control Applied to Biological Models. CRC Press, USA (2007)MATHCrossRef

Title: Dynamics and control of delayed rumor propagation through social networks
Authors: Moumita Ghosh
Samhita Das
Pritha Das
Publication date: 01-11-2021
Publisher: Springer Berlin Heidelberg
Published in: Journal of Applied Mathematics and Computing / Issue 5/2022
Print ISSN: 1598-5865
Electronic ISSN: 1865-2085
DOI: https://doi.org/10.1007/s12190-021-01643-5

Springer Professional

Abstract

Please log in to get access to your license.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Wirtschaft"

Springer Professional "Technik"

Other articles of this Issue 5/2022

Energy of interval-valued fuzzy graphs and its application in ecological systems

A novel approach for solving multi-term time fractional Volterra–Fredholm partial integro-differential equations

Optimality and duality for second-order interval-valued variational problems

Dynamically consistent nonstandard finite difference schemes for a virus-patch dynamic model

Orthogonal spline collocation method for the two-dimensional time fractional mobile-immobile equation

On sufficiency and duality theorems for nonsmooth semi-infinite mathematical programming problem with equilibrium constraints

Premium Partner