Dynamical analysis and optimal control of a stochastic SIAR model for computer viruses

Mathematical formulation of a stochastic computer viruses model with the application of optimal control and randomly noise transmission has been focused in this paper. For the ease of understanding, the model is divided into four different classes of susceptible, infected, antidotal and removed population. All four cases have been perturbed by the white noise. The existence and uniqueness for the global positive solution of the model are proved. The existence of the ergodicity of the stationary distribution is discussed by using the Lyapunov function and Has'minskii theory. The sufficient conditions for the extinction of the computer virus are presented. The optimal control strategies based on the least cost of prevention and control of computer viruses are carried out by using the stochastic maximum principle. The validity of the theoretical analysis results are verified by numerical simulation.