How many Americans are infected?

by quantize_me

How many Americans do you think are currently infected with SARS-CoV-2? How many Americans do you think will die? Write your answers down, this isn’t China, no bullshitting.

Trump’s estimation of 200,000 deaths with a peak in mid-April is almost certainly an underestimate. Information based on “confirmed cases” is a load of crap from both intentional and unintentional undertesting. There is however data that is relatively immune to fake news: deaths. The US is currently at 4,053 deaths. From this simple, clear data we can construct several hypotheses about how the illness will progress.

In this model, I will use three primary data inputs with low uncertainty to show you just how bad things are about to get.

  1. The time series of US deaths. NB: I used that data available yesterday and have not added yesterday’s 912 new deaths. Source: www.worldometers.info/coronavirus/country/us/
  2. A case fatality rate of 1%. This data comes from cruise ships where 100% of passengers were tested. This data is the best we have on case fatality, although the total numbers of infected are low enough to make this the largest source of model uncertainty. I also completely ignore the effect of overwhelmed hospitals in this analysis, if, as is likely, overwhelmed medical systems cause the case fatality rate to rise to WHO’s 3.4%, things will be much worse. Source: en.wikipedia.org/wiki/2020_coronavirus_pandemic_on_cruise_ships
  3. A time delay of three weeks between infection and death. This delay is approximately consistent with a median 6 days to symptoms and 13 days from pneumonia confirmation to death. Sources: en.wikipedia.org/wiki/Coronavirus_disease_2019 and wwwnc.cdc.gov/eid/article/26/6/20-0320_article . It is also consistent with many of the individual case reports that I have read, example, infected on 1/14, dead on 2/07 www.nytimes.com/interactive/2020/03/13/world/asia/coronavirus-death-life.html . I also include a two week delay analysis to help understand model error.

With this simple data, we can easily reconstruct how many Americans had the coronavirus three weeks prior. We take the daily new death data, multiply it by 100 (since 1% died) and add it to the total infections of the day three weeks before.

Estimating prior infections

From this computation, we can see that the current US confirmed case number is of 177,000 is an underestimate by about one half of the total infections THREE WEEKS AGO. This insight is the most important part of this post. We have way more cases right now than the vast majority realize. We’re not going to be able to Korea our way out of this any time soon.

Estimating growth of infections and deaths

Without massive intervention or a large proportion of the population infected we can use the growth in the number of deaths to estimate the growth rate of the infection. Below I fit an exponential curve to the growth of deaths to extract a parameter (lambda=3.54) for modeling future growth rate of the numbers of infected. I also included a fit for the last several days that possibly indicates a slight slowing of the growth rate. Note: All plots in this post are logarithmic.

Growth in number of deaths

Now, we can use the that growth to extrapolate how many more people have been infected since the ~314,000 on March 9th. Of course, that growth parameter has probably not remained constant. For that reason, I included some possible effects of social distancing whereby the growth halved or quartered starting on Monday, March 16th, when many business started suspending operations. I also assumed logistic growth so that the infection rate slows as more Americans are infected.

US infections, mid March through April

So, to answer one of the initial questions: There are between 1 million and 100 million US cases at present. That’s a huge range, but I am 95% sure that: there are between 4 and 20 million US infections at present.

Estimating Deaths

It gets ugly here. I know you’re all bears, but I hope you’re rooting for America and that we can pull a miracle. Lots of people will die.

Using the model for the number of infections, we can simply reverse the first process to find past number of infections to instead estimate the number of future deaths. Below, are estimates for total and daily deaths. The daily deaths will give us the best indication of which track we’re on in the future. There’s some discontinuity in that graph because I used the assumption that social distancing turned on all at once on 03/16, if we are on one of the lower tracks we will smooth into it in about a week’s time. So yesterday’s 912 deaths don’t mean much yet as far as predicting the evolution of the disease.

US Deaths, April through May

As is clearly evident, there is no way we’re only going to have 200,000 total deaths or a peak in two weeks unless social distancing is doing a much better job of quashing the spread than quartering it. Remember, this is also for 1% fatality rate, if deaths go up when hospitals are overwhelmed or because fat Americans die more, then there will be even more deaths. I am 80% sure that we will have 1 million deaths minimum over the next 3 months. Hopefully, we sacrifice the economy a bit to save lives, but don’t count on it.

Markets

There’s two main possibilities.

  1. Deaths peak between mid April and late May and that’s when you should sell your puts because we are at peak fear.
  2. We do a good job of suppressing the spread, but we have to stay in quarantine for many months. The economy will be slowly burned out and SPX goes (well) below 1800 in the late summer. June and later dated puts are going to do best here.

Positions:

Fun money: as many June puts as I can afford.

401(k): 100% cash

IRA: 70% cash, 30% $SH

 

 

Disclaimer: This information is only for educational purposes. Do not make any investment decisions based on the information in this article. Do you own due diligence.