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

Eng, G.

Early CoVID-19 growth often obeys: N{t}=N/Iexp[+K/ot], with K/o=[(ln2)/(t/dbl)], where t/dbl is the pandemic doubling time, prior to society-wide Social Distancing. Previously, we modeled Social Distancing with t/dbl as a linear function of time, where N[t]=1exp[+K/A t/(1+ gamma/o t)] is used here. Additional parameters besides {K/o,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: N(Z) = sum[m=0,M/F] g/m L/m(Z) exp[-Z] , R(Z) = sum[m=0,M/F] c/m L/m(Z) exp[-Z] , where N(Z) and Z[t] form an implicit N[t]=N(Z[t]) function, giving: G/o = [K/A / gamma/o ] , Z[t] = +[ G/o / (1+ gamma/ot) ] , rho[t] = [ gamma/o / G/o ] (Z^2) R(Z) , with L/m(Z) being the Laguerre Polynomials. At large M/F values, nearly arbitrary functions for N[t] and rho[t]=dN[t]/dt can be accommodated. How to determine {K/A, gamma/o} and the {g/m; m=(0,+M/F)} constants from any given N(Z) dataset is derived, with rho[t] set by: c/(M/F - k) = sum[m=0,k] g/m . The bing.com USA CoVID-19 data was analyzed using M/F=(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: = 5,009,677 (+/-) 269,450 (data to 5/3/20), and = 4,422,803 (+/-) 162,580 (data to 6/7/20), which compares the pre- and post-early May bing.com revisions. The CoVID-19 pandemic in Italy was examined next. The M/F=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).