IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v228y2025icp225-244.html
   My bibliography  Save this article

Global dynamics and numerical simulation of a modified epidemiological model for viral marketing on social networks

Author

Listed:
  • Hoang, Manh Tuan
  • Pham, Hoai Thu

Abstract

The aim of this work is to conduct a rigorous mathematical analysis for global dynamics and numerical simulation of a recognized viral marketing (VM) model, which is described by a system of ordinary differential equations (ODEs). We first establish positivity and boundedness of solutions and then investigate local and global asymptotic stability properties of possible equilibrium points. As an important consequence, complex dynamics of the VM model is determined fully.

Suggested Citation

  • Hoang, Manh Tuan & Pham, Hoai Thu, 2025. "Global dynamics and numerical simulation of a modified epidemiological model for viral marketing on social networks," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 228(C), pages 225-244.
    • Handle: RePEc:eee:matcom:v:228:y:2025:i:c:p:225-244
    DOI: 10.1016/j.matcom.2024.08.024
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475424003264
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2024.08.024?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Ping Jiang & Xiangbin Yan, 2017. "Stability analysis and control models for rumor spreading in online social networks," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 28(05), pages 1-22, May.
    2. Hoang, Manh Tuan, 2023. "Dynamical analysis of a generalized hepatitis B epidemic model and its dynamically consistent discrete model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 205(C), pages 291-314.
    3. Faragó, I. & Mosleh, R., 2023. "Some qualitative properties of the discrete models for malaria propagation," Applied Mathematics and Computation, Elsevier, vol. 439(C).
    4. Pasha, Syed Ahmed & Nawaz, Yasir & Arif, Muhammad Shoaib, 2023. "On the nonstandard finite difference method for reaction–diffusion models," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).
    5. Zhang, Yuhuai & Zhu, Jianjun, 2018. "Stability analysis of I2S2R rumor spreading model in complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 503(C), pages 862-881.
    6. Bhattacharya, Saumik & Gaurav, Kumar & Ghosh, Sayantari, 2019. "Viral marketing on social networks: An epidemiological perspective," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 478-490.
    7. Hoang, Manh Tuan, 2022. "Reliable approximations for a hepatitis B virus model by nonstandard numerical schemes," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 193(C), pages 32-56.
    8. Vargas-De-León, Cruz, 2011. "On the global stability of SIS, SIR and SIRS epidemic models with standard incidence," Chaos, Solitons & Fractals, Elsevier, vol. 44(12), pages 1106-1110.
    9. Huo, Liang’an & Wang, Li & Zhao, Xiaomin, 2019. "Stability analysis and optimal control of a rumor spreading model with media report," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 517(C), pages 551-562.
    10. Yang, Jianmei & Yao, Canzhong & Ma, Weicheng & Chen, Guanrong, 2010. "A study of the spreading scheme for viral marketing based on a complex network model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(4), pages 859-870.
    11. Steindorf, Vanessa & Srivastav, Akhil Kumar & Stollenwerk, Nico & Kooi, Bob W. & Aguiar, Maíra, 2022. "Modeling secondary infections with temporary immunity and disease enhancement factor: Mechanisms for complex dynamics in simple epidemiological models," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    12. Sahafizadeh, Ebrahim & Tork Ladani, Behrouz, 2018. "The impact of group propagation on rumor spreading in mobile social networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 506(C), pages 412-423.
    13. Adamu, Elias M. & Patidar, Kailash C. & Ramanantoanina, Andriamihaja, 2021. "An unconditionally stable nonstandard finite difference method to solve a mathematical model describing Visceral Leishmaniasis," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 187(C), pages 171-190.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Lu, Peng, 2019. "Heterogeneity, judgment, and social trust of agents in rumor spreading," Applied Mathematics and Computation, Elsevier, vol. 350(C), pages 447-461.
    2. Lu, Peng & Deng, Liping & Liao, Hongbing, 2019. "Conditional effects of individual judgment heterogeneity in information dissemination," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 335-344.
    3. Hoang, Manh Tuan, 2022. "Positivity and boundedness preserving nonstandard finite difference schemes for solving Volterra’s population growth model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 199(C), pages 359-373.
    4. Hajarathaiah, Koduru & Enduri, Murali Krishna & Anamalamudi, Satish, 2022. "Efficient algorithm for finding the influential nodes using local relative change of average shortest path," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 591(C).
    5. Chunru Li & Zujun Ma, 2022. "Dynamics Analysis and Optimal Control for a Delayed Rumor-Spreading Model," Mathematics, MDPI, vol. 10(19), pages 1-25, September.
    6. Lu, Peng & Yao, Qi & Lu, Pengfei, 2019. "Two-stage predictions of evolutionary dynamics during the rumor dissemination," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 517(C), pages 349-369.
    7. Yin, Fulian & Jiang, Xinyi & Qian, Xiqing & Xia, Xinyu & Pan, Yanyan & Wu, Jianhong, 2022. "Modeling and quantifying the influence of rumor and counter-rumor on information propagation dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    8. Sheikhahmadi, Amir & Nematbakhsh, Mohammad Ali & Shokrollahi, Arman, 2015. "Improving detection of influential nodes in complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 436(C), pages 833-845.
    9. Li, Shunjie & Zhang, Xuebing & An, Qi, 2024. "A rumor spreading multi-delay model with delay-dependent parameter," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 223(C), pages 34-49.
    10. Gupta, R.P. & Kumar, Arun, 2022. "Endemic bubble and multiple cusps generated by saturated treatment of an SIR model through Hopf and Bogdanov–Takens bifurcations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 197(C), pages 1-21.
    11. Gaurav, Kumar & Ghosh, Sayantari & Bhattacharya, Saumik & Singh, Yatindra Nath, 2019. "Ensuring the Spread of Referral Marketing Campaigns: A Quantitative Treatment," SocArXiv 6spnr_v1, Center for Open Science.
    12. Talal Daghriri & Michael Proctor & Sarah Matthews, 2022. "Evolution of Select Epidemiological Modeling and the Rise of Population Sentiment Analysis: A Literature Review and COVID-19 Sentiment Illustration," IJERPH, MDPI, vol. 19(6), pages 1-20, March.
    13. Jianhong Chen & Hongcai Ma & Shan Yang, 2023. "SEIOR Rumor Propagation Model Considering Hesitating Mechanism and Different Rumor-Refuting Ways in Complex Networks," Mathematics, MDPI, vol. 11(2), pages 1-22, January.
    14. Sheng Bin, 2023. "Social Network Emotional Marketing Influence Model of Consumers’ Purchase Behavior," Sustainability, MDPI, vol. 15(6), pages 1-17, March.
    15. Zhang, Jing & Wang, Xiaoli & Xie, Yanxi & Wang, Meihua, 2022. "Research on multi-topic network public opinion propagation model with time delay in emergencies," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 600(C).
    16. Wang, Feifei & Sun, Zejun & Gan, Quan & Fan, Aiwan & Shi, Hesheng & Hu, Haifeng, 2022. "Influential node identification by aggregating local structure information," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 593(C).
    17. Hoang, Manh Tuan, 2022. "Reliable approximations for a hepatitis B virus model by nonstandard numerical schemes," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 193(C), pages 32-56.
    18. Greenhalgh, D. & Liang, Y. & Mao, X., 2016. "Modelling the effect of telegraph noise in the SIRS epidemic model using Markovian switching," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 462(C), pages 684-704.
    19. Zhong, Haonan & Mahdavi Pajouh, Foad & Prokopyev, Oleg A., 2021. "Finding influential groups in networked systems: The most degree-central clique problem," Omega, Elsevier, vol. 101(C).
    20. Tomovski, Igor & Kocarev, Ljupčo, 2015. "Network topology inference from infection statistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 436(C), pages 272-285.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:matcom:v:228:y:2025:i:c:p:225-244. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/mathematics-and-computers-in-simulation/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.