Background: During the early stage of the COVID-19 pandemic, many countries implemented non-pharmaceutical interventions (NPIs) to control the transmission of SARS-CoV-2, the causative pathogen of COVID-19. Among those NPIs, stay-at-home and quarantine measures were widely adopted and enforced. Understanding the effectiveness of stay-at-home and quarantine measures can inform decision-making and control planning during the ongoing COVID-19 pandemic and for future disease outbreaks. Methods: In this study, we use mathematical models to evaluate the impact of stay-at-home and quarantine measures on COVID-19 spread in four cities that experienced large-scale outbreaks in the spring of 2020: Wuhan, New York, Milan, and London. We develop a susceptible-exposed-infected-removed (SEIR)-type model with components of self-isolation and quarantine and couple this disease transmission model with a data assimilation method. By calibrating the model to case data, we estimate key epidemiological parameters before lockdown in each city. We further examine the impact of stay-at-home and quarantine rates on COVID-19 spread after lockdown using counterfactual model simulations. Results: Results indicate that self-isolation of susceptible population is necessary to contain the outbreak. At a given rate, self-isolation of susceptible population induced by stay-at-home orders is more effective than quarantine of SARS-CoV-2 contacts in reducing effective reproductive numbers $$R_e$$R e . Variation in self-isolation and quarantine rates can also considerably affect the duration of outbreaks, attack rates and peak timing. We generate counterfactual simulations to estimate effectiveness of stay-at-home and quarantine measures. Without these two measures, the cumulative confirmed cases could be much higher than reported numbers within 40 days after lockdown in Wuhan, New York, Milan, and London. Conclusions: Our findings underscore the essential role of stay-at-home orders and quarantine of SARS-CoV-2 contacts during the early phase of the pandemic.

Reasonable scheduling of coke oven gas (COG) in steel industry will save fossil energy resources and increase gas consumption efficiency. In this study, a causal model-based scheduling approach is proposed to provide guidance for the coke oven gas scheduling. The causal relationship of the variables related to the gas tank level is discovered and the causal diagram is established, according to which the training sample is constructed and the predicting model of gas tank level is trained. Then, an objective function that considers the scheduling solution and its result is designed. To calculate the most reasonable solution, a modified particle swarm optimization algorithm is employed. The validation experiments are carried out by using practical data coming from a steel plant in China, where the gas tank level approaching the higher and the lower level zones are both considered. The human experience-based method and a data-based scheduling one are conducted as comparative studies. The results indicate that the proposed method is efficient for COG scheduling.