A “Tail” of Two Cities: Fatality-based Modeling of COVID-19 Evolution in New York City and Cook County, IL

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, R ₀ , and the mean time to removal from the infectious population, γ ⁻¹ , with γ ( R ₀ − 1)= 0.25(0.21) inverse days for NYC (Cook County). Equivalently, the initial doubling time was t _d = 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 R _t that declines monotonically from R ₀ to a smaller asymptotic value, R ₀ (1 − X ), with a parameterized functional form. The timing (mid-March) and duration (several days) of the transitions in R _t 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 R ₀ = 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 monotonically, 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 R _t plateaus at a value just above unity. For Cook County, the 95.45% credible intervals for the model parameters are not constrained by the case data and are much broader, R ₀ = 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, <inline-formula> <alternatives> <inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="20170506v2_inline1.gif"/> </alternatives> </inline-formula> , 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 <inline-formula> <alternatives> <inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="20170506v2_inline2.gif"/> </alternatives> </inline-formula> and on the asymptotic growth rate, and the impact in terms of fatalities will depend on the parameter f .