Seeking Best-Balanced Patch-Injecting Strategies through Optimal Control Approach

Abstract

To restrain escalating computer viruses, new virus patches must be constantly injected into networks. In this scenario, the patch-developing cost should be balanced against the negative impact of virus. This article focuses on seeking best-balanced patch-injecting strategies. First, based on a novel virus-patch interactive model, the original problem is reduced to an optimal control problem, in which (a) each admissible control stands for a feasible patch-injecting strategy and (b) the objective functional measures the balance of a feasible patch-injecting strategy. Second, the solvability of the optimal control problem is proved, and the optimality system for solving the problem is derived. Next, a few best-balanced patch-injecting strategies are presented by solving the corresponding optimality systems. Finally, the effects of some factors on the best balance of a patch-injecting strategy are examined. Our results will be helpful in defending against virus attacks in a cost-effective way.

Controlling Virus Spread Using an Intermittent Quarantine Strategy on Multiplex Networks

“…Zhao et al [41] developed a virus-information spreading model to design an optimal allocation strategy for patches. Once a virus spreads on the Internet, the simplest approach to stop the spreading is to bar Internet access until the virus is eliminated [42][43][44]. Because mathematical studies pertaining to information spreading dynamics are scarce, we herein propose a mathematical model to describe an interaction model based on multiplex networks.…”