In the classical infectious disease compartment model, the parameters are fixed. In reality, the probability of virus transmission in the process of disease transmission depends on the concentration of virus in the environment, and the concentration depends on the proportion of patients in the environment. Therefore, the probability of virus transmission changes with time. Then how to fit the parameters and get the trend of the parameters changing with time is the key to predict the disease course with the model. In this paper, based on the US COVID-19 epidemic statistics during calibration period, the parameters such as incidence rate and recovery rate are fitted by using the linear regression algorithm of machine science, and the laws of these parameters changing with time are obtained. Then a SIR model with time delay and vaccination is proposed, and the optimal control strategy of epidemic situation is analyzed by using the optimal control theory and Pontryagin maximum principle, which proves the effectiveness of the control strategy in restraining the spread of COVID-19. The numerical simulation results show that the time-varying law of the number of active cases obtained by our model basically conforms to the real changing law of the US COVID-19 epidemic statistics during calibration period. In addition, we have predicted the changes of the number of active cases in the COVID-19 epidemic in the United States over time in the future beyond the calibration cycle, and the predicted results are more in line with the actual epidemic data.
Neural models are widely being applied to headline generation. Template-based methods are one promising direction to overcome the shortcomings of the neural headline generation (NHG) model in generating duplicate or extra words. Previous work often retrieves related headlines from the training data and adopts them as the soft template. In this paper, we propose an alternative approach: we exploit the NHG model uncertainty to generate multiple diverse hypotheses and use these as soft-template to improve the model performance. Due to the computation resource limitation, we train our models on Alibaba Cloud, which is one of the largest public cloud providers in the world and operates in various countries. Experiments on English headline generation tasks show that incorporating multi-hypotheses as soft templates provides a significant performance boost over the strong baselines.
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