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With the advent of Internet-of-Things (IoT) age, IoT-based distributed denial-of-service (DDoS) attacks have become the mainstream of DDoS attacks. This paper is devoted to exploring the possibility of launching an IoT-based DDoS attack at an extremely low cost. First, a new DDoS attack architecture is proposed. Since the proposed architecture enjoys the advantages of zero management cost, good undetectability, and strong robustness, it is especially suited to resource-limited DDoS attackers. In this architecture and based on a novel botnet growth model, the optimal design of attack strategy is reduced to a variational problem, where the objective functional stands for the estimated expected impact of the DDoS attack associated with a DDoS attack strategy. Finally, the variational problem is resolved for three different types of DDoS defense strategies. This work deepens our understanding of IoT-based DDoS attacks. INDEX TERMS Cybersecurity, distributed denial-of-service (DDoS) attack, Internet-of-Things (IoT), DDoS attack architecture, botnet growth model, attack strategy, variational problem.

After-sale service is an integrable part of marketing activities. The after-sale service experience of a consumer can be measured by the dynamic maintenance (DM) strategy used by the merchant, i.e., the instantaneous fractions of the maintenance cost paid by the merchant in the total maintenance cost at all time. This paper aims to develop an optimal DM strategy for a word-of-mouth (WOM) marketing campaign. First, we propose an individual-based WOM propagation model in which the effect of the DM strategy is accounted for. Second, we convert the original problem into an optimal control problem, where the objective functional stands for the expected marketing profit, each optimal control stands for an optimal DM strategy. Third, we derive the optimality system for the optimal control problem. By solving the optimality system, we get a potential optimal control. Next, through comparative experiments we conclude that the DM strategy associated with the potential optimal control outperforms most DM strategies in terms of the expected marketing profit. Therefore, we recommend this potential DM strategy. Finally, we examine the effect of some factors on the expected marketing profit for the potential DM strategy. Our findings help to enhance the marketing profit of a WOM marketing campaign.

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.

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