SIRD Model of the Time Progression of Excess Deaths in NYC, the Total US, and Sweden Observed in the Spring of 2020

Abstract

Using a Susceptible-Infected-Recovered-Dead compartmental model approach, the time progression of excess deaths in NYC, the total US, and Sweden observed in the Spring of 2020 is modeled using variable-in-time second-order kinetics representing infection caused by social interaction followed by constant-in-time first-order kinetics representing the progression of the disease through various stages. The model is able to represent, at the $25 \%$ level, a combined dataset of weekly deaths per 100,000 population from NYC, the total US and Sweden as well as single points estimates of the number recovered from Covid-19 in NYC and Sweden. The time progression of the disease from infected to recovery or death is the same for the three populations, indicating that the disease underlying excess deaths is the same. According to this model, given this dataset, for the disease to be incapable of spreading in the population the fraction fRcrit of the population that are not susceptible (having antibodies) must be greater than 0.2 assuming social interactions as in NYC. This provides an estimate of the recovered fraction in the population needed for herd immunity, assuming the degree of closeness of social interactions as in NYC. For less close populations, the threshold for herd immunity would be lower.