I describe SIR modeling of the COVID-19 pandemic in two U.S. urban environments, New York City (NYC) and Cook County, IL, from onset through mid-June, 2020. Since testing was not widespread early in the pandemic in the U.S., I rely on public fatality data to estimate model parameters and use case data only as a lower bound. Fits to the first 20 days of data determine a degenerate combination of the basic reproduction number, R0, and the mean time to removal from the infectious population, 1/γ with γ(R0 − 1) = 0.25(0.21) inverse days for NYC (Cook County). Equivalently, the initial doubling time was td = 2.8(3.4) days for NYC (Cook). The early fatality data suggest that both locations had infections in early February. I model the mitigation measures implemented in mid-March in both locations (distancing, quarantine, isolation, etc) via a time-dependent reproduction number Rt that declines monotonically from R0 to a smaller asymptotic value, R0(1-X), with a parameterized functional form. The timing (mid-March) and duration (several days) of the transitions in Rt appear well determined by the data. With flat priors on model parameters and the lower bound from reported cases, the NYC fatality data imply 95.45% credible intervals of R0 = 2.6 − 2.9, social contact reduction X = 69 − 76% and infection fatality rate f = 1 − 1.5%, with 19 − 27% of the population asymptotically infected. The case data relative to daily deaths suggest that the reported case rate as a fraction of true case rate grew linearly, reaching a plateau around April 20 for both NYC and Cook County; the models also suggest that the late-time NYC reported case rate was comparable to the true rate, while for Cook County it remained an underestimate. For Cook County, the fatality evolution was qualitatively different from NYC: after mitigation measures were implemented, daily fatality counts reached a plateau for about a month before tailing off. This is consistent with an SIR model that exhibits "critical slowing-down", in which Rt plateaus at a value just above unity. For Cook County, the 95.45% credible intervals for the model parameters are much broader and shifted downward, R0 = 1.4 − 4.7, X = 26 − 54%, and f = 0.1 − 0.6% with 15 − 88% of the population asymptotically infected. Despite the apparently lower efficacy of its social contact reduction measures, Cook County has had significantly fewer fatalities per population than NYC, D∞/N = 100 vs. 270 per 100,000. In the model, this is attributed to the lower inferred IFR for Cook; an external prior pointing to similar values of the IFR for the two locations would instead chalk up the difference in D/N to differences in the relative growth rate of the disease. I derive a model-dependent threshold, Xcrit, for "safe" re-opening, that is, for easing of contact reduction that would not trigger a second wave; for NYC, the models predict that increasing social contact by more than 20% from post-mitigation levels will lead to renewed spread, while for Cook County the threshold value is very uncertain, given the parameter degeneracies. The timing of 2nd-wave growth will depend on the amplitude of contact increase relative to Xcrit and on the asymptotic growth rate, and the impact in terms of fatalities will depend on the parameter f .
Application of SEIR Model in COVID-19 and The Effect of Lockdown on Reducing The Number of Active Cases
