Approximate solutions of a SIR epidemiological model of computer viruses

Abstract

In the present study, a collocation procedure based upon two different polynomials (Bessel and Legendre) is presented to solve a modified nonlinear epidemiological model of computer viruses, which is a three-dimensional system of ordinary differential equations (ODEs) with quadratic nonlinearities. Representing the unknown solutions and their derivatives in the matrix forms along with the collocation points, the presented approximation algorithm transforms the given system of equations into a nonlinear matrix equation. In addition to direct Bessel or Legendre-collocation method, a combination of the idea of quasi-linearization and the Bessel/Legendre-collocation is applied to the original nonlinear system. The main benefit of the combined approach is the efficiency while keeping the accuracy. To assess the accuracy of the results, an error estimation based upon residual is performed. We evaluate the accuracy and performance of the proposed algorithm through some numerical experiments and comparison with different available alternative algorithms are also carried out in order to show the validity of the scheme. Overall, it was found that the combined approach indicated highly satisfactory performance and is more efficient compared with other numerical results.