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.
Highlights
Computer networks bring huge convenience to our work and life [1, 2]
We refer to a dynamic patch-injecting strategy that achieves the best balance between the two aspects as a best-balanced patch-injecting strategy, and we refer to the problem of seeking best-balanced patch-injecting strategies as the viruspatch tradeoff (VPT) problem
Based on a novel virus-patch interactive model, the original problem is reduced to an optimal control problem which we refer to as the VPT 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
Summary
Computer networks bring huge convenience to our work and life [1, 2]. digital viruses can propagate rapidly through computer networks, posing a severe threat to human society. To restrain evolving computer viruses, new virus patches must be constantly injected into networks. In this scenario, there is an obvious conflict between the patch-developing cost and the impact of virus; reducing the former would increase the latter, whereas mitigating the latter would enhance the former. The patch-developing cost should be balanced against the impact of virus. The effects of some factors on the best balance of a patch-injecting strategy are examined. Security and Communication Networks and solve the VPT control problem, respectively.
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