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

What does COVID-19 testing results really say? The real statistics concealed behind the accessible data

Accurate and comprehensive testing is crucial for practitioners to portray the pandemic. Without testing there is no data; yet, the exact number of infected people cannot be determined due to the lack of comprehensive testing. The number of seropositive for SARS-CoV-2 infection is obviously relative to the extent of testing. However, the true number of infections might be still far higher than the reported values. To compare the countries based on the number of seropositive for SARS-CoV-2 infection is misleading, as there may not be enough tests being carried out to properly monitor the outbreak. In this paper, we closely look through the COVID-19 testing results. Herein, we try to draw conclusions based on the reported data: first, the presence of a possible relationship between COVID-19 transition and patients' age will be assessed. Then, the COVID-19 case fatality rate (CFR) is compared with the age-demographic data for different countries. Based on the results, a method for estimating a lower bound (minimum) for the number of actual positive cases will be developed and validated. Results of this study have shown that CFR is a metric reflecting the spread of the virus, but is a factor of the extent of testing and does not necessarily show the real size of the outbreak. Moreover, no large difference in susceptibility by age has been found. The results suggest the similarity between the age distribution of COVID-19 and the population age-demographic is improving over the course of the pandemic. In addition, countries with lower CFRs have a more similar COVID-19 age distribution, which is a result of more comprehensive testing. Finally, a method for estimation of the real number of infected people based on the age distributions, reported CFRs, and the extent of testing will be developed and validated.

A simple mathematical tool to forecast COVID-19 cumulative case numbers

Objective

Mathematical models are known to help determine potential intervention strategies by providing an approximate idea of the transmission dynamics of infectious diseases. To develop proper responses, not only are more accurate disease spread models needed, but also those that are easy to use.

Materials and methods

As of July 1, 2020, we selected the 20 countries with the highest numbers of COVID-19 cases in the world. Using the Verhulst–Pearl logistic function formula, we calculated estimates for the total number of cases for each country. We compared these estimates to the actual figures given by the WHO on the same dates. Finally, the formula was tested for longer-term reliability at t = 18 and t = 40 weeks.

Results

The Verhulst–Pearl logistic function formula estimated the actual numbers precisely, with only a 0.5% discrepancy on average for the first month. For all countries in the study and the world at large, the estimates for the 40th week were usually overestimated, although the estimates for some countries were still relatively close to the actual numbers in the forecasting long term. The estimated number for the world in general was about 8 times that actually observed for the long term.

Conclusions

The Verhulst–Pearl equation has the advantage of being very straightforward and applicable in clinical use for predicting the demand on hospitals in the short term of 4–6 weeks, which is usually enough time to reschedule elective procedures and free beds for new waves of the pandemic patients.