Model to Describe Fast Shutoff of CoVID-19 Pandemic Spread

Early CoVID-19 growth obeys: [Formula], with Ko = [(ln 2)/(tdbl)], where tdbl is the pandemic growth doubling time. Given [Formula], the daily number of new CoVID-19 cases is [Formula]. Implementing society-wide Social Distancing increases the tdbl doubling time, and a linear function of time for tdbl was used in our Initial Model: O_FD O_INLINEFIG[Formula]C_INLINEFIGC_FD to describe these changes, with Go = [KA/{gamma}o]. However, this equation could not easily model some quickly decreasing{rho} [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 Zo[t] to allow exponential cutoffs: O_FD O_INLINEFIG[Formula]C_INLINEFIGC_FD provides a new Enhanced Initial Model (EIM), which significantly improves datafits, where [Formula]. Since large variations are present in{rho} data [t], these models were generalized into an orthogonal function series, to provide additional data fitting parameters: O_FD O_INLINEFIG[Formula]C_INLINEFIGC_FD Its first term can give No[t] or NE [t], for Z[t] [->] Zo[t] or Z[t] [->] Ze[t]. The Lm(Z) are Laguerre Polynomials, with L0(Z) = 1, and {gm; m = 0,MF} are constants derived from each dataset. When{rho} [t] = dN[t]/dt gradually decreases, using Zo[t] provided good datafits at small MF values, but was inadequate if{rho} [t] decreased faster. For those cases, ZE[t] was used in the above N(Z) series to give the most general Enhanced Orthogonal Function [EOF] model developed here. Even with MF = 0, qo = 0, this EOF model fit the Italy CoVID-19 data for{rho} [t] = dN[t]/dt fairly well. When the{rho} [t] post-peak behavior is not Gaussian, then ZE[t] with{delta} o = 0, qo = 0; which we call ZA[t], is also likely to be a sufficient extension of the Zo[t] model. The EOF model also can model a gradually decreasing{rho} [t] tail using small {{delta}o, qo} values [with 6 Figures].