Orthogonal Functions for Evaluating Social Distancing Impact on CoVID-19 Spread

Early CoVID-19 growth often obeys: [Formula], with Ko = [(ln 2)/(tdbl)], where tdbl is the pandemic doubling time, prior to society-wide Social Distancing. Previously, we modeled Social Distancing with tdbl as a linear function of time, where N [t] 1 {approx} exp[+KA t/ (1+,{gamma}ot)] is used here. Additional parameters besides {Ko,{gamma} o} are needed to better model different{rho} [t] = dN [t]/dt shapes. Thus, a new Orthogonal Function Model [OFM] is developed here using these orthogonal function series: O_FD O_INLINEFIG[Formula 1]C_INLINEFIGM_FD(1)C_FD where N (Z) and Z[t] form an implicit N [t] N (Z[t]) function, giving: O_FD O_INLINEFIG[Formula 2]C_INLINEFIGM_FD(2)C_FD with Lm(Z) being the Laguerre Polynomials. At large MF values, nearly arbitrary functions for N [t] and{rho} [t] = dN [t]/dt can be accommodated. How to determine {KA,{gamma} o} and the {gm; m = (0, +MF)} constants from any given N (Z) dataset is derived, with{rho} [t] set by: O_FD O_INLINEFIG[Formula 3]C_INLINEFIGM_FD(3)C_FD The bing com USA CoVID-19 data was analyzed using MF = (0, 1, 2) in the OFM. All results agreed to within about 10 percent, showing model robustness. Averaging over all these predictions gives the following overall estimates for the number of USA CoVID-19 cases at the pandemic end: O_FD O_INLINEFIG[Formula 4]C_INLINEFIGM_FD(4)C_FD which compares the pre- and post-early May bing com revisions. The CoVID-19 pandemic in Italy was examined next. The MF = 2 limit was inadequate to model the Italy{rho} [t] pandemic tail. Thus, regions with a quick CoVID-19 pandemic shutoff may have additional Social Distancing factors operating, beyond what can be easily modeled by just progressively lengthening pandemic doubling times (with 13 Figures).