Abstract
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.
Highlights
Introduction e smartInternet of ings (IoT), such as intelligent transportation, smart homes, smart grid, and the industrial revolution (i.e., Industry 4.0), are embedded in billions of wireless devices
We have proposed a new Heterogeneous Susceptible-Exposed-Infected-Recovered (HSEIR) model to investigate the malware propagation in wireless IoT networks, while considering the heterogeneity of infected wireless IoT devices
According to the ability of wireless devices on malware spreading, devices are divided into two different level groups in a fuzzy way
Summary
We describe the novel HSEIR model, which considers the heterogeneity of infected wireless devices in malware spreading. (i) Due to the partial efficiency of the vaccine, there is only η fraction of the vaccinated susceptible nodes that move to R state per unit time (ii) e remaining susceptible devices move to the exposed state, and the new exposed devices at time t are given by the expression aβ1I(t)S(t) + (1 − a) β2I(t)S(t), where β1 and β2 stand for the transmission coefficient of devices with weak spreading capability and strong capability and a and 1 − a represent the fraction of susceptible devices targeted by devices with weak spreading capability and strong capability, respectively (iii) e exposed devices transit into I with c when the malware begins actively, where c is the mean latent period (iv) Using some sufficient defense mechanisms, a portion of the exposed, infectious devices can recover at rates δ and φ, respectively:
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