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

## TL;DR

This paper compares semi-analytical methods for numerically approximating a modified non-linear SIR model of computer viruses, demonstrating the effectiveness of the Laplace-Adomian decomposition method over others.

## Contribution

It introduces a modified non-linear SIR model for computer viruses and compares the performance of DTM, LADM, and HATM methods for its numerical approximation.

## Key findings

- LADM outperforms HATM in accuracy.
- Residual error graphs validate the effectiveness of LADM.
- Phase portraits illustrate solution behaviors.

## 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.