Wireless Internet of Things (IoT) devices densely populate our daily life, but also attract many attackers to attack them. In this paper, we propose a new Heterogeneous Susceptible-Exposed-Infected-Recovered (HSEIR) epidemic model to characterize the effect of heterogeneity of infected wireless IoT devices on malware spreading. Based on the proposed model, we obtain the basic reproduction number, which represents the threshold value of diffusion and governs that the malware is diffusion or not. Also, we derive the malware propagation scale under different cases. These analyses provide theoretical guidance for the application of defense techniques. Numerical simulations validated the correctness and effectiveness of theoretical results. Then, by using Pontryagin’s Minimum Principle, optimal control strategy is proposed to seek time-varying cost-effective solutions against malware outbreaks. More numerical results also showed that some control strategies, such as quarantine and vaccination, should be taken at the beginning of the malware outbreak immediately and become less necessary after a certain period. However, the repairing and fixing strategy, for example applying antivirus patches, would be keep on going constantly.

中文翻译：

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无线物联网网络中恶意软件传播的建模和控制

无线物联网 (IoT) 设备在我们的日常生活中密集存在，但也吸引了许多攻击者对其进行攻击。在本文中，我们提出了一种新的异构易感暴露感染恢复（HSEIR）流行模型，以表征受感染无线物联网设备的异构性对恶意软件传播的影响。基于所提出的模型，我们获得了基本再现数，它代表了扩散的阈值，并决定了恶意软件是否扩散。此外，我们推导出了不同情况下的恶意软件传播规模。这些分析为防御技术的应用提供了理论指导。数值模拟验证了理论结果的正确性和有效性。然后，通过使用庞特里亚金的最小原理，提出了最佳控制策略，以寻求针对恶意软件爆发的时变成本效益解决方案。更多的数值结果还表明，一些控制策略，例如隔离和疫苗接种，应在恶意软件爆发开始时立即采取，并在一段时间后变得不必要。但是，修复和修复策略，例如应用防病毒补丁，将不断进行。