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Design of evolutionary finite difference solver for numerical treatment of computer virus propagation with countermeasures model

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  • Raja, Muhammad Asif Zahoor
  • Mehmood, Ammara
  • Ashraf, Sadia
  • Awan, Khalid Mahmood
  • Shi, Peng

Abstract

In the present study, a novel application of integrated evolutionary computing paradigm is presented for the analysis of nonlinear systems of differential equations representing the dynamics of virus propagation model in computer networks by exploiting the discretization strength of finite difference procedure, global search efficacy of genetic algorithms (GAs) aided with interior-point method (IPM) as efficient local search mechanism. Residual error based cost function is constructed by utilizing the effectiveness of approximation in mean square error sense and combined strength of GA-IPM is used as a viable optimization mechanism to find the solution of the problem. The proposed scheme is implemented for dynamical analysis of the model in terms of susceptible–infected and protected computer nodes by varying the probabilities of infections, countermeasures, curing and immunity while keeping connected and disconnected rates fixed. The statistical performance evaluated by means of deviations from reference Adams numerical results are practiced viably through performance metrics of accuracy and computational complexity to demonstrate the worth of integrated stochastic solver.

Suggested Citation

  • Raja, Muhammad Asif Zahoor & Mehmood, Ammara & Ashraf, Sadia & Awan, Khalid Mahmood & Shi, Peng, 2022. "Design of evolutionary finite difference solver for numerical treatment of computer virus propagation with countermeasures model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 193(C), pages 409-430.
    • Handle: RePEc:eee:matcom:v:193:y:2022:i:c:p:409-430
    DOI: 10.1016/j.matcom.2021.10.004
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    1. Zizhen Zhang & Huizhong Yang, 2013. "Hopf Bifurcation Analysis for a Computer Virus Model with Two Delays," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-18, November.
    2. Amador, Julia, 2014. "The stochastic SIRA model for computer viruses," Applied Mathematics and Computation, Elsevier, vol. 232(C), pages 1112-1124.
    3. Sabir, Zulqurnain & Wahab, Hafiz Abdul & Umar, Muhammad & Sakar, Mehmet Giyas & Raja, Muhammad Asif Zahoor, 2020. "Novel design of Morlet wavelet neural network for solving second order Lane–Emden equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 172(C), pages 1-14.
    4. Hasan, Bushra & Singh, Manmohan & Richards, David & Blicblau, Aaron, 2019. "Mathematical modelling of Zika virus as a mosquito-borne and sexually transmitted disease with diffusion effects," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 166(C), pages 56-75.
    5. Raja, Muhammad Asif Zahoor & Samar, Raza & Manzar, Muhammad Anwar & Shah, Syed Muslim, 2017. "Design of unsupervised fractional neural network model optimized with interior point algorithm for solving Bagley–Torvik equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 132(C), pages 139-158.
    6. Wu, Yingbo & Li, Pengdeng & Yang, Lu-Xing & Yang, Xiaofan & Tang, Yuan Yan, 2017. "A theoretical method for assessing disruptive computer viruses," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 482(C), pages 325-336.
    7. Pan, Wei & Jin, Zhen, 2018. "Edge-based modeling of computer virus contagion on a tripartite graph," Applied Mathematics and Computation, Elsevier, vol. 320(C), pages 282-291.
    8. Ji, Bingquan & Zhang, Luming, 2020. "A dissipative finite difference Fourier pseudo-spectral method for the Klein-Gordon-Schrödinger equations with damping mechanism," Applied Mathematics and Computation, Elsevier, vol. 376(C).
    9. Srivastav, Akhil Kumar & Yang, Junyuan & Luo, XiaoFeng & Ghosh, Mini, 2019. "Spread of Zika virus disease on complex network—A mathematical study," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 157(C), pages 15-38.
    10. Alemseged Gebrehiwot Weldeyesus & Jacek Gondzio, 2018. "A specialized primal-dual interior point method for the plastic truss layout optimization," Computational Optimization and Applications, Springer, vol. 71(3), pages 613-640, December.
    11. 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.
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    Cited by:

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    2. Yang, Wenbin & Li, Danqing & Chang, Xin, 2024. "Analysis and numerical simulation of computer virus propagation model based on limited resources," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 223(C), pages 494-508.
    3. Anwar, Nabeela & Ahmad, Iftikhar & Kiani, Adiqa Kausar & Shoaib, Muhammad & Raja, Muhammad Asif Zahoor, 2024. "Novel intelligent predictive networks for analysis of chaos in stochastic differential SIS epidemic model with vaccination impact," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 219(C), pages 251-283.

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