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SEI2RS malware propagation model considering two infection rates in cyber–physical systems

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  • Yu, Zhenhua
  • Gao, Hongxia
  • Wang, Dan
  • Alnuaim, Abeer Ali
  • Firdausi, Muhammad
  • Mostafa, Almetwally M.

Abstract

Cyber–physical systems (CPSs) are new types of intelligent systems that integrate computing, control, and communication technologies, and bridge cyberspace and physical world. CPSs are widely used in many security-critical areas, but they are vulnerable to virus infections and malicious code attacks, which can cause damage to their functions and security incidents. To study the influence of malware on CPSs, this paper proposes a Susceptible–Exposed–Infected1–Infected2–Removed (SEI2RS) model with different infection rates to study malware propagation in CPSs. First, we establish the nonlinear dynamic equation of malware propagation, and calculate the equilibria and basic reproduction number of the model. In addition, the local asymptotic stability and global asymptotic stability at the equilibria are proved by using Lyapunov theorem and Routh–Hurwitz criterion, and the transcritical bifurcation phenomenon is analyzed. Finally, we also carry out some simulations to simulate malware spreading in CPSs. The simulation results illustrate the existence of the equilibria, the stability and the transcritical bifurcation, which verify the effectiveness of the theoretical results.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:phsmap:v:597:y:2022:i:c:s0378437122001984
    DOI: 10.1016/j.physa.2022.127207
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    References listed on IDEAS

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    1. 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.
    2. Hosseini, Soodeh & Azgomi, Mohammad Abdollahi, 2019. "Dynamical analysis of a malware propagation model considering the impacts of mobile devices and software diversification," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 526(C).
    3. Xia, Ling-Ling & Jiang, Guo-Ping & Song, Bo & Song, Yu-Rong, 2015. "Rumor spreading model considering hesitating mechanism in complex social networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 437(C), pages 295-303.
    4. 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).
    5. Khan, Muhammad Altaf & Khan, Yasir & Islam, Saeed, 2018. "Complex dynamics of an SEIR epidemic model with saturated incidence rate and treatment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 493(C), pages 210-227.
    6. Jianguo Ren & Yonghong Xu & Jiming Liu, 2014. "Global Bifurcation of a Novel Computer Virus Propagation Model," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-6, April.
    7. José Roberto C. Piqueira & Cristiane M. Batistela, 2019. "Considering Quarantine in the SIRA Malware Propagation Model," Mathematical Problems in Engineering, Hindawi, vol. 2019, pages 1-8, November.
    8. Yu, Zhenhua & Arif, Robia & Fahmy, Mohamed Abdelsabour & Sohail, Ayesha, 2021. "Self organizing maps for the parametric analysis of COVID-19 SEIRS delayed model," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
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