IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v12y2024i6p835-d1355726.html
   My bibliography  Save this article

Deriving Exact Mathematical Models of Malware Based on Random Propagation

Author

Listed:
  • Rodrigo Matos Carnier

    (Information Systems Architecture Research Division, National Institute of Informatics, 2-1-2 Hitotsubashi, Chiyoda City, Tokyo 101-8430, Japan)

  • Yue Li

    (Department of Electrical and Computer Engineering, Yokohama National University, 79-5 Tokiwadai, Hodogaya Ward, Yokohama 240-8501, Japan)

  • Yasutaka Fujimoto

    (Department of Electrical and Computer Engineering, Yokohama National University, 79-5 Tokiwadai, Hodogaya Ward, Yokohama 240-8501, Japan)

  • Junji Shikata

    (Graduate School of Environment and Information Sciences, Yokohama National University, 79-5 Tokiwadai, Hodogaya Ward, Yokohama 240-8501, Japan)

Abstract

The advent of the Internet of Things brought a new age of interconnected device functionality, ranging from personal devices and smart houses to industrial control systems. However, increased security risks have emerged in its wake, in particular self-replicating malware that exploits weak device security. Studies modeling malware epidemics aim to predict malware behavior in essential ways, usually assuming a number of simplifications, but they invariably simplify the single most important subdynamics of malware: random propagation. In our previous work, we derived and presented the first exact mathematical model of random propagation, defined as the subdynamics of propagation of a malware model. The propagation dynamics were derived for the SIS model in discrete form. In this work, we generalize the methodology of derivation and extend it to any Markov chain model of malware based on random propagation. We also propose a second method of derivation based on modifying the simplest form of the model and adjusting it for more complex models. We validated the two methodologies on three malware models, using simulations to confirm the exactness of the propagation dynamics. Stochastic errors of less than 0.2% were found in all simulations. In comparison, the standard nonlinear model of propagation (present in ∼95% of studies) has an average error of 5% and a maximum of 9.88% against simulations. Moreover, our model has a low mathematical trade-off of only two additional operations, being a proper substitute to the standard literature model whenever the dynamical equations are solved numerically.

Suggested Citation

  • Rodrigo Matos Carnier & Yue Li & Yasutaka Fujimoto & Junji Shikata, 2024. "Deriving Exact Mathematical Models of Malware Based on Random Propagation," Mathematics, MDPI, vol. 12(6), pages 1-28, March.
  • Handle: RePEc:gam:jmathe:v:12:y:2024:i:6:p:835-:d:1355726
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/12/6/835/pdf
    Download Restriction: no

    File URL: https://www.mdpi.com/2227-7390/12/6/835/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Yang, Lu-Xing & Draief, Moez & Yang, Xiaofan, 2016. "The optimal dynamic immunization under a controlled heterogeneous node-based SIRS model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 450(C), pages 403-415.
    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. Yonghong Xu & Jianguo Ren, 2016. "Propagation Effect of a Virus Outbreak on a Network with Limited Anti-Virus Ability," PLOS ONE, Public Library of Science, vol. 11(10), pages 1-15, October.
    2. Ren, Jianguo & Xu, Yonghong, 2017. "A compartmental model for computer virus propagation with kill signals," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 486(C), pages 446-454.
    3. Li, Pengdeng & Yang, Xiaofan & Yang, Lu-Xing & Xiong, Qingyu & Wu, Yingbo & Tang, Yuan Yan, 2018. "The modeling and analysis of the word-of-mouth marketing," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 493(C), pages 1-16.
    4. Jichao Bi & Lu-Xing Yang & Xiaofan Yang & Yingbo Wu & Yuan Yan Tang, 2018. "A tradeoff between the losses caused by computer viruses and the risk of the manpower shortage," PLOS ONE, Public Library of Science, vol. 13(1), pages 1-12, January.
    5. Pan, Cheng & Yang, Lu-Xing & Yang, Xiaofan & Wu, Yingbo & Tang, Yuan Yan, 2018. "An effective rumor-containing strategy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 500(C), pages 80-91.
    6. Piqueira, José Roberto C. & Cabrera, Manuel A.M. & Batistela, Cristiane M., 2021. "Malware propagation in clustered computer networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 573(C).
    7. Zhang, Tianrui & Yang, Lu-Xing & Yang, Xiaofan & Wu, Yingbo & Tang, Yuan Yan, 2017. "Dynamic malware containment under an epidemic model with alert," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 470(C), pages 249-260.
    8. Yang, Dingda & Liao, Xiangwen & Shen, Huawei & Cheng, Xueqi & Chen, Guolong, 2018. "Dynamic node immunization for restraint of harmful information diffusion in social networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 503(C), pages 640-649.
    9. Kar, T.K. & Nandi, Swapan Kumar & Jana, Soovoojeet & Mandal, Manotosh, 2019. "Stability and bifurcation analysis of an epidemic model with the effect of media," Chaos, Solitons & Fractals, Elsevier, vol. 120(C), pages 188-199.
    10. Zhang, Xulong & Gan, Chenquan, 2018. "Global attractivity and optimal dynamic countermeasure of a virus propagation model in complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 1004-1018.
    11. Li, Pengdeng & Yang, Xiaofan & Wu, Yingbo & He, Weiyi & Zhao, Pengpeng, 2018. "Discount pricing in word-of-mouth marketing: An optimal control approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 505(C), pages 512-522.

    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:gam:jmathe:v:12:y:2024:i:6:p:835-:d:1355726. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.