Optimal control strategy for a novel computer virus propagation model on scale-free networks

• Propose a novel SLBOS computer virus propagation model on scale-free networks.
• Obtain the spreading threshold and global stability criterions.
• Investigate existence of an optimal control for the control problem.
• Some numerical simulations are given to illustrate the main results.

This paper aims to study the combined impact of reinstalling system and network topology on the spread of computer viruses over the Internet. Based on scale-free network, this paper proposes a novel computer viruses propagation model—SLBOSmodel. A systematic analysis of this new model shows that the virus-free equilibrium is globally asymptotically stable when its spreading threshold is less than one; nevertheless, it is proved that the viral equilibrium is permanent if the spreading threshold is greater than one. Then, the impacts of different model parameters on spreading threshold are analyzed. Next, an optimally controlled SLBOS epidemic model on complex networks is also studied. We prove that there is an optimal control existing for the control problem. Some numerical simulations are finally given to illustrate the main results.