Optimal control strategies for a computer network under virus threat

Abstract

This study proposes different optimal control strategies to eliminate the damage of virus propagation in a computer network with a minimum cost of installing anti-virus software. The model discussed to be developed is a fractional-order SEIR epidemiological model. Unlike the existing studies on the model, it has been considered that the recovered computers may malfunction due to any mechanical reason, and the model has been developed accordingly. In addition, unit consistency for the model is provided. Although there are a limited number of studies in the literature, the control variable affects the equilibrium points and thus the stability of the controlled system. Therefore, the reproduction number is recalculated for the controlled system. Before the optimal control problem is formulated, the existence of optimal control is proved. Then, the optimal system is obtained using Hamiltonian formalism. The numerical solutions of the optimal system are achieved by the fractional Euler method combined with the forward–backward sweep algorithm. The graphs drawn with MATLAB software show the efficiency of the fractional parameter for different control scenarios. Comparing the three proposed control strategies, it is clear that Strategy 1 is the most effective anti-virus installation strategy. In other words, if an anti-virus software is installed on both infected computers and susceptible computers connected to exposed and infected computers, virus propagation in the network can be prevented quickly as intended. Moreover, this is achieved by minimizing the cost of installing an antivirus program, thanks to the optimal control strategy.