Backward bifurcation, basic reinfection number and robustness of an SEIRE epidemic model with reinfection

Recent evidences show that individuals who recovered from COVID-19 can be reinfected. However, this phenomenon has rarely been studied using mathematical models. In this paper, we propose an SEIRE epidemic model to describe the spread of the epidemic with reinfection. We obtain the important thresholds R-0 (the basic reproduction number) and R-c (a threshold less than one). Our investigations show that when R-0 > 1, the system has an endemic equilibrium, which is globally asymptotically stable. When R-c < R-0 < 1, the epidemic system exhibits bistable dynamics. That is, the system has backward bifurcation and the disease cannot be eradicated. In order to eradicate the disease, we must ensure that the basic reproduction number R0 is less than Rc. The basic reinfection number is obtained to measure the reinfection force, which turns out to be a new tipping point for disease dynamics. We also give definition of robustness, a new concept to measure the difficulty of completely eliminating the disease for a bistable epidemic system. Numerical simulations are carried out to verify the conclusions.

Augmented Multicenter Graph Convolutional Network for COVID-19 Diagnosis

Chest computed tomography (CT) scans of coronavirus 2019 (COVID-19) disease usually come from multiple datasets gathered from different medical centers, and these images are sampled using different acquisition protocols. While integrating multicenter datasets increases sample size, it suffers from inter-center heterogeneity. To address this issue, we propose an augmented multicenter graph convolutional network (AM-GCN) to diagnose COVID-19 with steps as follows. First, we use a 3-D convolutional neural network to extract features from the initial CT scans, where a ghost module and a multitask framework are integrated to improve the network's performance. Second, we exploit the extracted features to construct a multicenter graph, which considers the intercenter heterogeneity and the disease status of training samples. Third, we propose an augmentation mechanism to augment training samples which forms an augmented multicenter graph. Finally, the diagnosis results are obtained by inputting the augmented multi-center graph into GCN. Based on 2223 COVID-19 subjects and 2221 normal controls from seven medical centers, our method has achieved a mean accuracy of 97.76%. The code for our model is made publicly.(1)