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

Bundit Unyong

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 obtained 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.

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