Initial Model for USA CoVID-19 Resurgence

Early CoVID-19 growth obeys: <inline-formula> <alternatives> <inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="20196063v1_inline1.gif"/> </alternatives> </inline-formula> , with K _o = [(ln 2)/( t _dbl )], where t _dbl is the pandemic growth doubling time . Given <inline-formula> <alternatives> <inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="20196063v1_inline2.gif"/> </alternatives> </inline-formula> , the daily number of new CoVID-19 cases is <inline-formula> <alternatives> <inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="20196063v1_inline3.gif"/> </alternatives> </inline-formula> . 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 : <disp-formula id="ueqn1"> <alternatives> <graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="20196063v1_ueqn1.gif" position="float" orientation="portrait"/> </alternatives> </disp-formula> to describe these changes, where the [t]-axis is time-shifted from the <inline-formula> <alternatives> <inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="20196063v1_inline4.gif"/> </alternatives> </inline-formula> –axis back to the pandemic start, and G _o ≡ [ K _A / γ _o ]. While this N _o [t] successfully modeled the USA CoVID-19 progress from 3/2020 to 6/2020, this equation could not easily model some quickly decreasing ρ [ t ] cases (“ fast pandemic shutoff “), indicating that a second process was involved. This situation was most evident in the initial CoVID-19 data from China, South Korea , and Italy . Modifying Z _o [ t ] to allow exponential cutoffs: <disp-formula id="ueqn2"> <alternatives> <graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="20196063v1_ueqn2.gif" position="float" orientation="portrait"/> </alternatives> </disp-formula> resulted in an Enhanced Initial Model (EIM) that significantly improved data fits for these cases.

After 6/2020, many regions of the USA “ opened up ”, loosening their Social Distancing requirements, which led to a sudden USA CoVID-19 Resurgence . Extrapolating the USA N _o [ t ] 3/2020-6/2020 results to 9/2020 as an Initial Model Baseline (IMB) , and subtracting this IMB from the newer USA data gives a Resurgence Only function, which is analyzed here. This USA CoVID-19 Resurgence function differs significantly from the N _o [t] IMB functional form, but it was well-modeled by the N _A [ t ] fast pandemic shutoff function. These results indicate that: (a) the gradual increase in t _dbl doubling time from society-wide shut-downs is likely due to eliminating of a large number of population gathering points that could have enabled CoVID-19 spread; and (b) having a non-zero δ _o fast pandemic shutoff is likely due to more people wearing masks more often [with 12 Figures ].