A Simple Mathematical Model for Estimating the Inflection Points of COVID-19 Outbreaks

Ma, Zhanshan (Sam)

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 (Tmax) & maximal infection number (Imax) 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 (Imax) and another is proposed to determine the corresponding inflection time point (Tmax). Results: We successfully estimated the inflection points [Imax, Tmax] for most provinces (≈ 85%) in China with error rates <5% in both Imax and Tmax. 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.