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Study of the stability of a SEIRS model for computer worm propagation

Author

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  • Hernández Guillén, J.D.
  • Martín del Rey, A.
  • Hernández Encinas, L.

Abstract

Nowadays, malware is the most important threat to information security. In this sense, several mathematical models to simulate malware spreading have appeared. They are compartmental models where the population of devices is classified into different compartments: susceptible, exposed, infectious, recovered, etc. The main goal of this work is to propose an improved SEIRS (Susceptible–Exposed–Infectious–Recovered–Susceptible) mathematical model to simulate computer worm propagation. It is a continuous model whose dynamic is ruled by means of a system of ordinary differential equations. It considers more realistic parameters related to the propagation; in fact, a modified incidence rate has been used. Moreover, the equilibrium points are computed and their local and global stability analyses are studied. From the explicit expression of the basic reproductive number, efficient control measures are also obtained.

Suggested Citation

  • Hernández Guillén, J.D. & Martín del Rey, A. & Hernández Encinas, L., 2017. "Study of the stability of a SEIRS model for computer worm propagation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 479(C), pages 411-421.
    • Handle: RePEc:eee:phsmap:v:479:y:2017:i:c:p:411-421
    DOI: 10.1016/j.physa.2017.03.023
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    References listed on IDEAS

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    1. Sharma, Natasha & Gupta, Arvind Kumar, 2017. "Impact of time delay on the dynamics of SEIR epidemic model using cellular automata," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 471(C), pages 114-125.
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    Cited by:

    1. Yu, Zhenhua & Gao, Hongxia & Wang, Dan & Alnuaim, Abeer Ali & Firdausi, Muhammad & Mostafa, Almetwally M., 2022. "SEI2RS malware propagation model considering two infection rates in cyber–physical systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 597(C).
    2. Jia, Pingqi & Wang, Chao & Zhang, Gaoyu & Ma, Jianfeng, 2019. "A rumor spreading model based on two propagation channels in social networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 524(C), pages 342-353.
    3. Hosseini, Soodeh & Azgomi, Mohammad Abdollahi, 2018. "The dynamics of an SEIRS-QV malware propagation model in heterogeneous networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 512(C), pages 803-817.
    4. Gao, Qingwu & Zhuang, Jun, 2020. "Stability analysis and control strategies for worm attack in mobile networks via a VEIQS propagation model," Applied Mathematics and Computation, Elsevier, vol. 368(C).

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