Visualizing the features of inflection point shown on a temporal bar graph using the data of COVID-19 pandemic

Exponential-like infection growth leading to peaks (denoted by inflection points [IP] or turning points) is usually the hallmark of infectious disease outbreaks, including coronaviruses. To determine the IPs of the novel coronavirus (COVID-19), we applied the item response theory model to detect phase transitions for each country/region and characterize the IP feature on the temporal bar graph (TBG).

The IP (using the item difficulty parameter to locate) was verified by the differential equation in calculus and interpreted by the TBG with 2 virtual and real empirical data (i.e., from Collatz conjecture and COVID-19 pandemic in 2020). Comparisons of IPs, R2, and burst strength [BS = ln() denoted by the infection number at IP(Nip) and the item slope parameter(a) in item response theory were made for countries/regions and continents on the choropleth map and the forest plot.

We found that the evolution of COVID-19 on the TBG makes the data clear and easy to understand, the shorter IP (=53.9) was in China and the longest (=247.3) was in Europe, and the highest R2 (as the variance explained by the model) was in the US, with a mean R2 of 0.98. We successfully estimated the IPs for countries/regions on COVID-19 in 2020 and presented them on the TBG.

Temporal visualization is recommended for researchers in future relevant studies (e.g., the evolution of keywords in a specific discipline) and is not merely limited to the IP search in COVID-19 pandemics as we did in this study.