Model to Describe Fast Shutoff of CoVID-19 Pandemic Spread

Eng, Genghmun

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 {rho}{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 + {gamma}/o t) ] = exp(+G/o) exp( - Z/o[t] ) , to describe these changes, with G/o = [K/A / {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 Z/o[t] to allow exponential cutoffs: Z/E[t] = +[G/o / (1 + {gamma}/o t) ] [exp( - {delta}/o t - q/o t^2 ] = Z/o[t] [exp( - {delta}/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 {rho}/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 {rho}[t]=dN[t]/dt gradually decreases, using Z/o[t] provided good datafits at small M/F values, but was inadequate if {rho}[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 {rho}[t] = dN[t]/dt fairly well. When the {rho}[t] post-peak behavior is not Gaussian, then Z/E[t] with {delta}/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 {rho}[t] tail using small {{delta}/o, q/o} values [with 6 Figures].