A Simple Mathematical Model for Estimating the Inflection Points of COVID-19 Outbreaks
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Abstract
Background
Exponential-like infection growths leading to peaks (which could be the inflection points or turning points) are usually the hallmarks of infectious disease outbreaks including coronaviruses. To predict the inflection points, i.e ., inflection time ( T max ) & maximal infection number ( I max ) of the novel coronavirus (COVID-19), we adopted a trial and error strategy and explored a series of approaches from simple logistic modeling (that has an asymptomatic line) to sophisticated tipping point detection techniques for detecting phase transitions but failed to obtain satisfactory results.
Method
Inspired by its success in diversity-time relationship (DTR), we apply the PLEC (power law with exponential cutoff) model for detecting the inflection points of COVID-19 outbreaks. The model was previously used to extend the classic species-time relationship (STR) for general DTR (Ma 2018), and it has two “secondary” parameters (computed from its 3 parameters including power law scaling parameter w , taper-off parameter d to overwhelm virtually exponential growth ultimately, and a parameter c related to initial infections): one that was originally used for estimating the potential or ‘dark’ biodiversity is proposed to estimate the maximal infection number ( I max ) and another is proposed to determine the corresponding inflection time point ( T max ).
Results
We successfully estimated the inflection points [ I max , T max ] for most provinces (≈85%) in China with error rates <5% in both I max and T max . We also discussed the constraints and limitations of the proposed approach, including ( i ) sensitive to disruptive jumps, ( ii ) requiring sufficiently long datasets, and ( iii ) limited to unimodal outbreaks.
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SciScore for 10.1101/2020.03.25.20043893: (What is this?)
Please note, not all rigor criteria are appropriate for all manuscripts.
Table 1: Rigor
NIH rigor criteria are not applicable to paper type.Table 2: Resources
No key resources detected.
Results from OddPub: We did not detect open data. We also did not detect open code. Researchers are encouraged to share open data when possible (see Nature blog).
Results from LimitationRecognizer: We detected the following sentences addressing limitations in the study:In this section, by analyzing the failures of PLEC case by case, we try to uncover the model’s limitations. We first examine the failure exposed in previous Tables 1 & 2. In Tables 1 & 2, the PLEC model for Shandong province performed badly with error rates about 11% was apparently due to the sudden discovery of approximately 200 cases …
SciScore for 10.1101/2020.03.25.20043893: (What is this?)
Please note, not all rigor criteria are appropriate for all manuscripts.
Table 1: Rigor
NIH rigor criteria are not applicable to paper type.Table 2: Resources
No key resources detected.
Results from OddPub: We did not detect open data. We also did not detect open code. Researchers are encouraged to share open data when possible (see Nature blog).
Results from LimitationRecognizer: We detected the following sentences addressing limitations in the study:In this section, by analyzing the failures of PLEC case by case, we try to uncover the model’s limitations. We first examine the failure exposed in previous Tables 1 & 2. In Tables 1 & 2, the PLEC model for Shandong province performed badly with error rates about 11% was apparently due to the sudden discovery of approximately 200 cases in a local prison on a single day (Feb 20), which was approximately 1/5 of the total number in the province. The model for Gansu province also performed badly with error rates of 36%, apparently due to 33 inputs from the overseas between March 4th and 8th, approximately 1/3 of the total number in the province. These individual cases suggest that the PLEC modeling can be sensitive to certain disruptive increases, in particular, to the increases that occupy disproportionally large proportion of the total numbers. This may be considered as the first limitation of the PLEC model. On the positive side, excluding the inaccuracies from these disruptive increases as well as the individual cases of Taiwan and Tibet, the PLEC model actually performed exceptionally well, reaching success rates mostly exceeding 95%. We also fitted the PLEC model to the infection datasets of at least 14 countries (top 14 in terms of the infection numbers until March 15th) as well as the worldwide total infection number, and total worldwide infection number excluding China. Overall, in a majority of the cases, the PLEC model failed to obtain satisfactory predictions for the ...
Results from TrialIdentifier: No clinical trial numbers were referenced.
Results from Barzooka: We did not find any issues relating to the usage of bar graphs.
Results from JetFighter: We did not find any issues relating to colormaps.
Results from rtransparent:- Thank you for including a conflict of interest statement. Authors are encouraged to include this statement when submitting to a journal.
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