A simple model for the total number of SARS-CoV-2 infections on a national level.

This study aimed to identify an appropriate simple mathematical model to fit the number of coronavirus disease 2019 (COVID-19) cases at the national level for the early portion of the pandemic, before significant public health interventions could be enacted. The total number of cases for the COVID-19 epidemic over time in 28 countries was analysed and fit to several simple rate models. The resulting model parameters were used to extrapolate projections for more recent data. While the Gompertz growth model (mean R2 = 0.998) best fit the current data, uncertainties in the eventual case limit introduced significant model errors. However, the quadratic rate model (mean R2 = 0.992) fit the current data best for 25 (89%) countries as determined by R2 values of the remaining models. Projection to the future using the simple quadratic model accurately forecast the number of future total number of cases 50% of the time up to 10 days in advance. Extrapolation to the future with the simple exponential model significantly overpredicted the total number of future cases. These results demonstrate that accurate future predictions of the case load in a given country can be made using this very simple model.

Assays for allantoinase.

Allantoinase hydrolyzes allantoin, a purine metabolite and a nitrogen transport molecule in plants, to form allantoic acid. The standard enzyme assay involves acid-catalyzed product decomposition to form urea and glyoxylate, reaction of glyoxylate with phenylhydrazine, and oxidative conversion of phenylhydrazone to 1, 5-diphenylformazan that is measured colorimetrically. When used with crude cell extracts this assay is problematic and its complexity is a hindrance to detailed enzyme characterization; thus, three alternative assays were developed. In the first assay, 2, 4-dinitrophenylhydrazine was reacted with allantoate-derived glyoxylate and the concentration of hydrazone was measured directly by its absorbance at 450 nm. This assay exhibited enhanced reproducibility compared to the standard method and entailed fewer steps, but was 3-fold less sensitive. The second assay combined allantoate decomposition and glyoxylate reaction with o-phenylenediamine to yield a quinoxalone that was detected by its absorbance at 340 nm. This one-step method was the least error prone of those examined, but was more than 10-fold less sensitive than the standard assay. The third assay involved urease-catalyzed hydrolysis of allantoate-derived urea, followed by reaction of the released ammonia to form indophenol. This was the most laborious of the assays, but was more sensitive than the standard method.