Hidden Parameters Impacting Resurgence of SARS-CoV-2 Pandemic

The spread of the SARS-CoV-2 virus has had an enormous impact on the world's health and socioeconomic system. While a lockdown, which severely limits the movement of the population, has been implemented in March 2020 and again in late 2020, the psychological and economic costs are severe. Removal of these restrictions had varying degrees of success. To understand the impact of health policy, we study parameters that contribute to the resurgence of the virus upon removal of lockdown. Mandates and guidance on removal of lockdown varied across the United States. Along with social distancing mandates, active infections and the fraction of susceptible population remaining are identified as important factors in the resurgence of infections. We consider an epidemiological model that incorporates the set of people in lockdown, a population that is released linearly upon removal of lockdown. This model further incorporates a dynamic social distance metric based on progression of the infections; it reflects the dynamic propensity of infection spread based on the current infections relative to the susceptible population. It is determined that this model fits the data with more accuracy than the standard SIR model, where data on growth of infections, hospitalizations and death was obtained from 24 counties in multiple US states, along with a categorization of the lockdown removal policies after the first lockdown. Mobility data from the counties illustrates the relationship between policy mandates and visits to establishments like restaurants and personal care establishments. Model parameters are used to determine the rate at which the susceptible population increases, due to removal of lockdown, to fit the rate of infections. We also studied infection growth in the 24 US counties with respect to a two-phase release policy derived from CDC guidelines and compared against strategies that delay the removal of lockdown. Results: The efficacy of the lockdown removal policy is measured via a ratio, Peak Infection Ratio (PIR). This ratio evaluates to less than one for counties where social distancing measures were mandated and which delayed complete re-opening of closed spaces like restaurants and personal care establishments. For other counties this ratio is greater than one. Our results also show that not all counties respected the two-phase policy rule that we devised using CDC guidelines. Furthermore, delaying reopening in these counties by 30 days would have resulted in at least 40% less infections. Conclusions: Results illustrate that guidelines for deciding when lockdown rules are to be relaxed should consider the current state of the actively infectious population and the remaining susceptible population which are hidden parameters that are deducible from epidemiological models such as the one we consider, the SIR-SD-L model. This contrasts with policies that measure the reduction in growth of infections; the growth rate being correlated primarily to immediate non-pharmaceutical (NPI) interventions. This is especially true for counties where the growth rate of the virus is initially slow and misleading. Emphasis and mandates on social distancing is critical. Funding Statement: Research sponsored by NSF. grant No. 2028274. Declaration of Interests: None to declare.