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Numerical approximation of modified non-linear SIR model of computer viruses

Samad Noeiaghdam

TL;DR

This work addresses the non-linear SIR-based model of computer-virus spread and demonstrates the use of two semi-analytical approaches, the Differential Transform Method ($DTM$) and the Laplace-Adomian Decomposition Method ($LADM$), to obtain accurate approximate solutions. By deriving recurrence relations and Adomian polynomials for the nonlinear terms, the authors generate nth-order approximations and compare performance against the Homotopy Analysis Transform Method ($HATM$) through residual-error metrics and phase portraits. The numerical results show that $LADM$ provides higher accuracy than $DTM$ and $HATM$ across $n=5,10,15$, with clear convergence evidenced by decreasing residuals and consistent dynamics in the phase spaces. The study offers robust, efficient tools for analyzing computer-virus propagation models, with potential applications in cybersecurity modeling and defense planning.

Abstract

In this paper, the non-linear modified epidemiological model of computer viruses is illustrated. For this aim, two semi-analytical methods, the differential transform method (DTM) and the Laplace-Adomian decomposition method (LADM) are applied. The numerical results are estimated for different values of iterations and compared to the results of the LADM and the homotopy analysis transform method (HATM). Also, graphs of residual errors and phase portraits of approximate solutions for $n=5,10,15$ are demonstrated. The numerical approximations show the performance of the LADM in comparison to the LADM and the HATM.

Numerical approximation of modified non-linear SIR model of computer viruses

TL;DR

This work addresses the non-linear SIR-based model of computer-virus spread and demonstrates the use of two semi-analytical approaches, the Differential Transform Method () and the Laplace-Adomian Decomposition Method (), to obtain accurate approximate solutions. By deriving recurrence relations and Adomian polynomials for the nonlinear terms, the authors generate nth-order approximations and compare performance against the Homotopy Analysis Transform Method () through residual-error metrics and phase portraits. The numerical results show that provides higher accuracy than and across , with clear convergence evidenced by decreasing residuals and consistent dynamics in the phase spaces. The study offers robust, efficient tools for analyzing computer-virus propagation models, with potential applications in cybersecurity modeling and defense planning.

Abstract

In this paper, the non-linear modified epidemiological model of computer viruses is illustrated. For this aim, two semi-analytical methods, the differential transform method (DTM) and the Laplace-Adomian decomposition method (LADM) are applied. The numerical results are estimated for different values of iterations and compared to the results of the LADM and the homotopy analysis transform method (HATM). Also, graphs of residual errors and phase portraits of approximate solutions for are demonstrated. The numerical approximations show the performance of the LADM in comparison to the LADM and the HATM.

Paper Structure

This paper contains 5 sections, 29 equations, 5 figures, 5 tables.

Table of Contents

  1. Introduction
  2. Differential transform method
  3. Laplace-Adomian decomposition method
  4. Numerical Illustration
  5. Conclusion

Figures (5)

  • Figure 1: Comparison between error functions of LADM, DTM and HATM for $S_{5}(t), I_{5}(t), R_{5}(t)$.
  • Figure 2: Comparison between error functions of LADM, DTM and HATM for $S_{10}(t), I_{10}(t), R_{10}(t)$.
  • Figure 3: Comparison between error functions of LADM, DTM and HATM for $S_{15}(t), I_{15}(t), R_{15}(t)$.
  • Figure 4: Phase portraits of $S_{10}(t), I_{10}(t), R_{10}(t)$ by using the LADM.
  • Figure 5: Phase portraits of $S_{10}(t), I_{10}(t), R_{10}(t)$ by using the DTM.