Model to Describe Fast Shutoff of CoVID-19 Pandemic Spread

  1. Genghmun Eng

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Abstract

Early CoVID-19 growth obeys: N{t*}=N/I\ exp[+K/o\ t*], with K/o\ = [(ln 2) / (t/dbl\)], where t/dbl\ is the pandemic growth doubling time. Given N{t*}, the daily number of new CoVID-19 cases is ρ{t*}=dN{t*}/dt*. Implementing society-wide Social Distancing increases the t/dbl\ doubling time, and a linear function of time for t/dbl\ was used in our Initial Model: N/o\[t] = 1 exp[+K/A\ t / (1 + γ/o\ t) ] = exp(+G/o\) exp( - Z/o\[t] ) , to describe these changes, with G/o\ = [K/A\ / γ/o\]. However, this equation could not easily model some quickly decreasing ρ[t] cases, indicating that a second Social Distancing process was involved. This second process is most evident in the initial CoVID-19 data from China, South Korea, and Italy. The Italy data is analyzed here in detail as representative of this second process. Modifying Z/o\[t] to allow exponential cutoffs: Z/E\[t] = +[G/o\ / (1 + γ/o\ t) ] [exp( - δ/o\ t - q/o\ t^2 ] = Z/o\[t] [exp( - δ/o\ t - q/o\ t^2 ] , provides a new Enhanced Initial Model (EIM), which significantly improves datafits, where N/E\[t] = exp(+G/o\) exp( - Z/E\[t] ). Since large variations are present in ρ/data\[t], these models were generalized into an orthogonal function series, to provide additional data fitting parameters: N(Z) = Sum{m = (0, M/F\)} g/m\ L/m\(Z) exp[-Z]. Its first term can give N/o\[t] or N/E\[t], for Z=Z/o\[t] or Z=Z/E\[t]. The L/m\(Z) are Laguerre Polynomials, with L/0\(Z)=1, and {g/m\; m= (0, M/F\)} are constants derived from each dataset. When ρ[t]=dN[t]/dt gradually decreases, using Z/o\[t] provided good datafits at small M/F\ values, but was inadequate if ρ[t] decreased faster. For those cases, Z/E\[t] was used in the above N(Z) series to give the most general Enhanced Orthogonal Function [EOF] model developed here. Even with M/F\=0 and q/o\=0, this EOF model fit the Italy CoVID-19 data for ρ[t] = dN[t]/dt fairly well. When the ρ[t] post-peak behavior is not Gaussian, then Z/E\[t] with δ/o\≠0, q/o\=0; which we call Z/A\[t], is also likely to be a sufficient extension of the Z/o\[t] model. The EOF model also can model a gradually decreasing ρ[t] tail using small {δ/o\, q/o\} values [with 6 Figures].

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    SciScore for 10.1101/2020.08.07.20169904: (What is this?)

    Please note, not all rigor criteria are appropriate for all manuscripts.

    Table 1: Rigor

    Institutional Review Board Statementnot detected.
    Randomizationnot detected.
    Blindingnot detected.
    Power Analysisnot detected.
    Sex as a biological variablenot detected.

    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).

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    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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    • No protocol registration statement was detected.

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  2. Version published to 10.1101/2020.08.07.20169904v1 on medRxiv