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

Zhanshan (Sam) Ma

Inspired by the exponential-like growth of infections leading to peaks, which seems to be a hallmark of many infectious disease outbreaks including COVID-19 and SARS (Rivers et al. 2019 , Li et al. 2020 , Thompson 2020 , Ma 2020 , we try the PLEC (power law with exponential cutoff) model for detecting the inflection points in the time series data of COVID-19. The PLEC model (function) starts with power function increase (near exponential growth usually) and it has an exponential decay term that acts as taper-off parameter to eventually overwhelm the power law behavior at very large value of independent variable. The PLEC model was previously used to describe the classic species-area relationship (SAR) in biogeography (Plotkin et al. 2000 , Ulrich & Buszko 2003 , and later used for extending the classic SAR and STR (species-time relationship) to general diversity-area relationship (DAR) and diversity-time relationship (DTR) (Ma 2018a (Ma , 2018b (Ma , 2019 . Furthermore, Ma (2018a Ma ( , 2018b Ma ( , 2019 derived the formula to estimate the maximal accrual diversity (MAD) in space (area), time, and/or spatiotemporal settings, which may also be used to estimate potential diversity (also known as "dark" diversity).