Hidden Parameters Impacting Resurgence of SARS-CoV-2 Pandemic^*

The spread of the COVID-19 virus has had an enormous impact on the world’s health and socioeconomic system. While lockdowns, which severely limit the movement of the population, have been implemented in March 2020 and again recently, the psychological and economic cost are severe. Removal of these restrictions occurred with varying degrees of success.

To study the resurgence of the virus in some communities we consider an epidemiological model, SIR-SD-L, that incorporates introduction of new population due to the removal of lockdown and identify parameters that impact the spread of the virus. This compartmental model of the epidemic incorporates a social distance metric based on progression of the infections; it models the dynamic propensity of infection spread based on the current infections relative to the susceptible population. The model is validated using data on growth of infections, hospitalizations and death, considering 24 counties in multiple US states and a categorization of the lockdown removal policies after the first lockdown. Model parameters, which include a compartment for the isolated population, are used to determine the rate at which the susceptible population increases to fit the rate of infections. Along with social distancing mandates, we identify active infections and the susceptible population as important factors in the resurgence of infections. We measure the efficacy of the lockdown removal policy via a ratio, PIR, which evaluates to less than 1 for counties where social distancing measures were mandated and which delayed complete re-opening of closed spaces like bars and restaurants. For other counties this ratio is greater than 1.

We also studied infection growth in the 24 US counties with respect to a release policy derived from CDC guidelines and compared against strategies that delay the removal of lockdown.

Our results illustrate that guidelines for deciding when lockdown rules are to be relaxed should consider the current state of the infectious population and the remaining susceptible population, hidden parameters that are deducible from models such as SIR-SD-L, and not limit policy considerations to the rate of new infections alone. This is especially true for counties where the growth rate of the virus is initially slow and misleading. Emphasis on social distancing is critical.