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

Early CoVID-19 growth often obeys: <inline-formula> <alternatives> <inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="20143149v1_inline1.gif"/> </alternatives> </inline-formula> , with K _o = [(ln 2)/( 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 ] 1 ≈ exp[+ K _A t / (1+, γ _o t )] is used here. Additional parameters besides { K _o , γ _o } are needed to better model different ρ [ t ] = dN [ t ]/ dt shapes. Thus, a new Orthogonal Function Model [ OFM ] is developed here using these orthogonal function series: <disp-formula id="ueqn1"> <alternatives> <graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="20143149v1_ueqn1.gif" position="float" orientation="portrait"/> </alternatives> </disp-formula> where N ( Z ) and Z [ t ] form an implicit N [ t ] N ( Z [ t ]) function, giving: <disp-formula id="ueqn2"> <alternatives> <graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="20143149v1_ueqn2.gif" position="float" orientation="portrait"/> </alternatives> </disp-formula> with L _m ( Z ) being the Laguerre Polynomials . At large M _F values, nearly arbitrary functions for N [ t ] and ρ [ t ] = dN [ t ]/ dt can be accommodated. How to determine { K _A , γ _o } and the { g _m ; m = (0, + M _F )} constants from any given N ( Z ) dataset is derived, with ρ [ t ] set by: <disp-formula id="ueqn3"> <alternatives> <graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="20143149v1_ueqn3.gif" position="float" orientation="portrait"/> </alternatives> </disp-formula>

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: <disp-formula id="ueqn4"> <alternatives> <graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="20143149v1_ueqn4.gif" position="float" orientation="portrait"/> </alternatives> </disp-formula> 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 ρ [ 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 ).