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To address the threat of drones intruding into high-security areas, the real-time detection of drones is urgently required to protect these areas. There are two main difficulties in real-time detection of drones. One of them is that the drones move quickly, which leads to requiring faster detectors. Another problem is that small drones are difficult to detect. In this paper, firstly, we achieve high detection accuracy by evaluating three state-of-the-art object detection methods: RetinaNet, FCOS, YOLOv3 and YOLOv4. Then, to address the first problem, we prune the convolutional channel and shortcut layer of YOLOv4 to develop thinner and shallower models. Furthermore, to improve the accuracy of small drone detection, we implement a special augmentation for small object detection by copying and pasting small drones. Experimental results verify that compared to YOLOv4, our pruned-YOLOv4 model, with 0.8 channel prune rate and 24 layers prune, achieves 90.5% mAP and its processing speed is increased by 60.4%. Additionally, after small object augmentation, the precision and recall of the pruned-YOLOv4 almost increases by 22.8% and 12.7%, respectively. Experiment results verify that our pruned-YOLOv4 is an effective and accurate approach for drone detection.

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a b s t r a c tA stochastic susceptible-infectious-recovered epidemic model with nonlinear incidence rate is formulated to discuss the effects of temporary immunity, vaccination, and Lévy jumps on the transmission of diseases. We first determine the existence of a unique global positive solution and a positively invariant set for the stochastic system. Sufficient conditions for extinction and persistence in the mean of the disease are then achieved by constructing suitable Lyapunov functions. Based on the analysis, we conclude that noise intensity and the validity period of vaccination greatly influence the transmission dynamics of the system.