MATHEMATICAL MODEL FOR MALICIOUS OBJECTS IN COMPUTER NETWORK WITH THE EFFECT OF EDUCATION CAMPAIGN

Abstract

In this paper, a modified SI1I2R model for the transmission of malicious objects in a computer network with the effect of the education campaign and its applications were proposed and analyzed. The standard method is used to analyze the behaviors of the proposed model. The results show that there were two equilibrium points; virus disease free and virus endemic equilibrium point. The qualitative results are depended on a basic reproductive number(R0). We btained the basic reproductive number by using the next generation method and finding the spectral radius. Routh-Hurwitz criteria are used for determining the stabilities of the model. If R0<1, then the virus disease-free equilibr ium point is local asymptotically stable, but if R0>1, then the endemic equilibrium is local
asymptotically stable. In order to get more good results the perturbation iteration method to be applied and derived the iteration scheme with the  algorithm that includes a combination of perturbation expansion and Taylor series expansion. The result from the numerical solutions of the models be shown and compared for supporting the analytic results.