Estimation of the case fatality rate based on stratification for the COVID-19 outbreak.

This work is motivated by the recent worldwide pandemic of the novel coronavirus disease (COVID-19). When an epidemiological disease is prevalent, estimating the case fatality rate, the proportion of deaths out of the total cases, accurately and quickly is important as the case fatality rate is one of the crucial indicators of the risk of a disease. In this work, we propose an alternative estimator of the case fatality rate that provides more accurate estimate during an outbreak by reducing the downward bias (underestimation) of the naive CFR, the proportion of deaths out of confirmed cases at each time point, which is the most commonly used estimator due to the simplicity. The proposed estimator is designed to achieve the availability of real-time update by using the commonly reported quantities, the numbers of confirmed, cured, deceased cases, in the computation. To enhance the accuracy, the proposed estimator adapts a stratification, which allows the estimator to use information from heterogeneous strata separately. By the COVID-19 cases of China, South Korea and the United States, we numerically show the proposed stratification-based estimator plays a role of providing an early warning about the severity of a epidemiological disease that estimates the final case fatality rate accurately and shows faster convergence to the final case fatality rate.

Improvement of activated sludge dewaterability by humus soil induced bioflocculation.

Effects of humus soil particles on the dewaterability of activated sludge were investigated. Cations leaching increased proportionally with the dosage of humus soil, and the leaching was not significant after 2 h. Divalent cations, Ca2+ and Mg2+, leaching from the humus soil played an important role in improving dewaterability of the biological sludge. On the contrary, dewaterability was not affected or slightly deteriorated by the monovalent cations, K+ and Na+ leached from the humus soil. Improvement in dewaterability of the sludge by addition of humus soil was higher than that of equivalent cations mixture. It seemed that the decrease of supracolloidal bio-particles (1 to 100 microm in diameter) resulted in diminishing of the blinding effect on cake and filter medium. SRF (specific resistance to filtration) of the humus soil added sludge varied in parallel with the M/D (monovalent to divalent cation) ratio, and the M/D ratio could be utilized as a useful tool for evaluation of the sludge dewatering characteristics. Long-term effects of humus soil on the improvement of activated sludge dewaterability were clearly identified by continuous operation results of a bench-scale MLE (Modified Ludzack Ettinger) system combined with a humus soil contactor. On the other hand, dewaterability of the control sludge was only slightly improved by a decrease in M/D ratio of the wastewater influent.