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# New York City epidemic: quantifying lockdown effect from simulation… plus some insight on the proportion of infected

A CovModel 1.5 simulation of the Covid-19 epidemic in New York City was run to simulate death incidence up to 13 April 2020. The initial reproduction number was found Ro=3.2. We easily explained a peak in daily death of 670 occuring last Friday 10 April assuming a sharp reduction in R factor happening on 24 March (obviously interpreted to represent the City getting into lockdown, on 20 March). Interestingly, our model estimates that 12.8% of the population was infected by Sars-CoV-2 on 28 March. This figure compares very well with a recently published figure of 15.4%, the proportion of women patients testing positive to the virus as part of a systematic test before being admitted to a local obstetrical hospital.

#### Model

For this scenario, we used a “severe to infected” ratio rho of 0.015 and a “fatality to severe” theta of 0.14. The assumption is therefore an ultimate Infection Fatality Rate (IFR) of 0.21%. As a reminder, any assumption on IFR would have resulted in a model match of death curve, but with a different outcome on proportion having contacted the virus. An IFR of 0.21% is currently considered on the high side, hence pessimistic on immunity (See the excellent page on IFR by University of Oxford CEBM https://www.cebm.net/covid-19/global-covid-19-case-fatality-rates/).

Population is 8.4 M. Death data taken from Git Hub JHU repository, for “NY City, NY”. We hope the two refer to same territory…

Model is matched on death incidence and cumulative death curve only. Match is easily obtained using : Ro=3.2 for the initial slope of cumulative death curve in logarithmic scale and 9 Feb 2020 as the date of first introduction. Thereafter, by trial an error, death curve is “bent” using the R factor schedule in Table 1.

Figures 1 and 2 below provide usual simulated curve results. In Figure 3, we show a curve newly programmed in version 1.5 of our model: the simulated seroprevalence curve. More details are in Figure legends.

Model predicts ultimate death toll of 11940 at end of May, following a sharp decline in daily death incidence now-on. This is subject to confinement measures remaining in place and R staying at 1.5.

We find that R is on the high side compared to Italy, France, Spain, South Korea, all showing a value lower than or equal to 1.2 after lockdown. Beware that the definition of R is intrinsic to a particular model and may not be comparable from study to study without modification.

In “Universal Screening for SARS-CoV-2 in Women Admitted for Delivery” published yesterday by Desmond Sutton et al., Columbia University Irving Medical Center, New York, NY, (https://www.nejm.org/doi/full/10.1056/NEJMc2009316) authors found that among 215 obstetrical patients presenting for delivery, between March 22 and April 4, at a hospital situated in NYC North of Manhattan, 15.4% tested positive to Sars-CoV-2.

We found it interesting that this number compared very well with our simulation results for 28 March: infected proportion of population estimated 12.8%.

The proportion not susceptible anymore (having been in contact with virus) is higher, estimated 42.5% on 28 March. It jumps to 65% today (14 April), demonstrating strong dynamics of the epidemic in New York City.

The implication of such dynamics is important: New York City is the only territory, among those we have studied, that may approach acquired group immunity at end of this spring outbreak (the theoretical threshold being calculated 69%). The direct relationship between high fatality rate in New York City and acquired immunity is obvious, since cumulative death is proportional to total number of persons having contacted the virus.

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