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Two time-delay dynamic model on the transmission of malicious signals in wireless sensor network

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  • Keshri, Neha
  • Mishra, Bimal Kumar

Abstract

Deployed in a hostile environment, motes of a Wireless sensor network (WSN) could be easily compromised by the attackers because of several constraints such as limited processing capabilities, memory space, and limited battery life time etc. While transmitting the data to their neighbour motes within the network, motes are easily compromised due to resource constraints. Here time delay can play an efficient role to reduce the adversary effect on motes. In this paper, we propose an epidemic model SEIR (Susceptible–Exposed–Infectious–Recovered) with two time delays to describe the transmission dynamics of malicious signals in wireless sensor network. The first delay accounts for an exposed (latent) period while the second delay is for the temporary immunity period due to multiple worm outbreaks. The dynamical behaviour of worm-free equilibrium and endemic equilibrium is shown from the point of stability which switches under some threshold condition specified by the basic reproduction number. Our results show that the global properties of equilibria also depends on the threshold condition and that latent and temporary immunity period in a mote does not affect the stability, but they play a positive role to control malicious attack. Moreover, numerical simulations are given to support the theoretical analysis.

Suggested Citation

  • Keshri, Neha & Mishra, Bimal Kumar, 2014. "Two time-delay dynamic model on the transmission of malicious signals in wireless sensor network," Chaos, Solitons & Fractals, Elsevier, vol. 68(C), pages 151-158.
  • Handle: RePEc:eee:chsofr:v:68:y:2014:i:c:p:151-158
    DOI: 10.1016/j.chaos.2014.08.006
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    References listed on IDEAS

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    1. Jianguo Ren & Yonghong Xu & Yongchang Zhang & Yongquan Dong & Guosheng Hao, 2012. "Dynamics of a Delay-Varying Computer Virus Propagation Model," Discrete Dynamics in Nature and Society, Hindawi, vol. 2012, pages 1-12, August.
    2. Chunjin Wei & Lansun Chen, 2008. "A Delayed Epidemic Model with Pulse Vaccination," Discrete Dynamics in Nature and Society, Hindawi, vol. 2008, pages 1-12, March.
    3. Xiaofan Yang & Lu-Xing Yang, 2012. "Towards the Epidemiological Modeling of Computer Viruses," Discrete Dynamics in Nature and Society, Hindawi, vol. 2012, pages 1-11, November.
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    Cited by:

    1. Zizhen Zhang & Soumen Kundu & Ruibin Wei, 2019. "A Delayed Epidemic Model for Propagation of Malicious Codes in Wireless Sensor Network," Mathematics, MDPI, vol. 7(5), pages 1-18, May.
    2. Keshri, Ajit Kumar & Mishra, Bimal Kumar & Rukhaiyar, Bansidhar Prasad, 2020. "When rumors create chaos in e-commerce," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    3. Zizhen Zhang & Fangfang Yang & Wanjun Xia, 2019. "Hopf Bifurcation Analysis of a Synthetic Drug Transmission Model with Time Delays," Complexity, Hindawi, vol. 2019, pages 1-17, November.
    4. Akgül, Ali & Fatima, Umbreen & Iqbal, Muhammad Sajid & Ahmed, Nauman & Raza, Ali & Iqbal, Zafar & Rafiq, Muhammad, 2021. "A fractal fractional model for computer virus dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 147(C).
    5. Guiyun Liu & Zhimin Peng & Zhongwei Liang & Xiaojing Zhong & Xinhai Xia, 2022. "Analysis and Control of Malware Mutation Model in Wireless Rechargeable Sensor Network with Charging Delay," Mathematics, MDPI, vol. 10(14), pages 1-28, July.

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