Abstract:
A computer virus is a program that can replicate, multiply and infect from one program to another, user to user, computer to computer, and network to network. The mathematical model approach can be used to predict the dynamics of spread of computer viruses on a network. The model of spread of computer viruses on network is based on the fact that computer will be infected by infected computers and exposed computers and some computers that are in a vulnerable and exposed status can obtain immunity with antivirus capabilities. In this paper, we present a fractional mathematical model of the spread of computer viruses on networks with fractional order. The dynamic behavior of this model is investigated. First, we determine the stability of the equilibrium point for the fractional model. Based on the model analysis, we gained two points of equilibrium, the equilibrium point is virus-free computer and equilibrium point endemic virus computer . We also obtain basic reproduction rate, which determine the existence and stability os the equilibrium point. The equilibrium point is virus-free computer is stable asymptotic locally if basic reproduction number less than one and equilibrium endemic virus computer point stable asymptotic locally if basic reproduction number more than one. Next, we analyze the sensitivity of the parameters that most influence the spread of computer viruses. Finally, we carry out numerical simulations with variations ? to illustrate analytical result.
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