Samad Noeiaghdam - Department of Mathematics, Central Tehran Branch, Islamic Azad University, Tehran, Iran.
Mohammad Ali Fariborzi Araghi - Department of Mathematics, Central Tehran Branch, Islamic Azad University, Tehran, Iran.

Susceptible-Infected-Recovered (SIR) computer virus propagation model is one of the important and applicable models to analyze, track and protect the computer systems against the computer viruses. The aim of this research is to present the novel and efficient method to solve the SIR model of computer viruses. This method is obtained by combining the homotopy analysis method and the Laplace transformations which is called the homotopy analysis transform method. The convergence theorem is proved to show the abilities of the proposed approach to solve the nonlinear epidemiological model of computer viruses. Several ℏ-curves are demonstrated to show the convergence regions for various number of terms. In order to exhibit the precision of the scheme, the residual error functions are applied and by using these functions the optimal values of convergence parameter are obtained. The graphs of residual errors based on the optimal values of ℏ demonstrate the efficiency of the suggested approach

Susceptible-Infected-Recovered model, Modified epidemiological model, Computer virus, Homotopy analysis method, Laplace transformation