Disruptive computer viruses have inflicted huge economic losses. This paper addresses the development of a cost-effective dynamic control strategy of disruptive viruses. First, the development problem is modeled as an optimal control problem. Second, a criterion for the existence of an optimal control is given. Third, the optimality system is derived. Next, some examples of the optimal dynamic control strategy are presented. Finally, the performance of actual dynamic control strategies is evaluated.

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One of the major threats to cybersecurity is the emergence of new computer viruses. By emergence of new viruses, the cybersecurity companies assign a team of security experts and programmers to study the behavior of the virus and develop the corresponding antivirus program to secure networks. Sometimes, more than one new virus is identified that requires the cybersecurity team to make a tradeoff on the allocation of programmers, and thus leads to two-antivirus-program development problem under doublevirus attack. In this paper, we propose DOWNHILL algorithm to address the outlined challenge. We model the time evolution of the expected state of the network as a differential dynamical system to measure the total loss caused by the viruses. Then, we propose a DOWNHILL algorithm, three heuristic algorithms and a random algorithm to solve the problem, respectively. We study the computational complexities of the proposed algorithms as well. Through numerous comparative experiments, we confirm the DOWNHILL algorithm is the most effective method to this problem. Finally, the influence of different factors on the DOWNHILL strategy and its potential total loss are also researched.INDEX TERMS Computer virus, antivirus, dynamic model, constrained optimization.