Initial Model for the Impact of Social Distancing on CoVID-19 Spread

The initial stages of the CoVID-19 coronavirus pandemic all around the world exhibit a nearly exponential rise in the number of infections with time. Planners, governments, and agencies are scrambling to figure out “ How much? How bad? ” and how to effectively treat the potentially large numbers of simultaneously sick people. Modeling the CoVID-19 pandemic using an exponential rise implicitly assumes a nearly unlimited population of uninfected persons ( “dilute pandemic” ). Once a significant fraction of the population is infected ( “saturated pandemic” ), an exponential growth no longer applies. A new model is developed here, which modifies the standard exponential growth function to account for factors such as Social Distancing . A Social Mitigation Parameter [SMP] α _S is introduced to account for these types of society-wide changes, which can modify the standard exponential growth function, as follows: <disp-formula id="eqn1"> <alternatives> <graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="20091207v1_eqn1.gif" position="float" orientation="portrait"/> </alternatives> </disp-formula>

The doubling-time t _dbl = (In 2)/ K _o can also be used to substitute for K _o , giving a { t _dbl , α _S } parameter pair for comparing to actual CoVID-19 data. This model shows how the number of CoVID-19 infections can self-limit before reaching a saturated pandemic level. It also provides estimates for: (a) the timing of the pandemic peak , (b) the maximum number of new daily cases that would be expected, and (c) the expected total number of CoVID-19 cases. This model shows fairly good agreement with the presently available CoVID-19 pandemic data for several individual States, and the for the USA as a whole ( 6 Figures ), as well as for various countries around the World ( 9 Figures ). An augmented model with two Mitigation Parameters, α _S and β _S , is also developed, which can give better agreement with the daily new CoVID-19 data. Data-to-model comparisons also indicate that using α _S by itself likely provides a worst-case estimate, while using both α _S and β _S likely provides a best-case estimate for the CoVID-19 spread.