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This work is concerned with the numerical modeling of susceptible-latent-breakingout-quarantine-susceptible (SLBQRS) computer virus dynamics. The SLBQRS epidemic system is solved with three finite difference methods, one is proposed nonstandard finite difference (NSFD) method and the other two are well known forward Euler finite difference (FD) method and Runge-Kutta finite difference method of order 4 (RK-4). The proposed NSFD method preserves all the essential conditions of the continuous system while RK-4 method and forward Euler method fail to preserve some of its essential conditions like positivity, convergence to the true steady states of the continuous system. The convergence analysis of the proposed NSFD method is also performed. Bifurcation value of infection coefficient for the system is also find out.