6. Weekly Forecasts of COVID-19 Death and Prevalence

(3/24/20) Still no evidence of a turnover in the death and infection rate, but we’re only one week into serious social distancing in the U.S.

In this post we update our death and prevalence/incidence statistics of a week ago (Post 3). This post has a lot of data so don’t get intimidated or bogged down in the detail. I will summarize the key points and refer you to where in the Tables and Figures to look. At the end of this post are plots of the cumulative reported deaths each day for eight countries and a description on how they lead to the values in the Table below.

Before we begin our worldwide assessment from the above Table, let’s look at the conditions in the U.S. as exemplified by the plots below.

In just one week the cumulative deaths in the U.S. have increased from 69 (3/16/20) to 471 (3/23/20). This is nearly a 7-fold increase and represents a doubling about every 2.5 days. Further the daily rate is increasing at a staggering clip with a daily death rate now exceeding 100. With these trends in mind we can now summarize the above Table. Key observations are:

  • The number of deaths in the U.S. is forecasted to exceed 1,000 over the next week and if no downtrend in the incidence of COVID-19 occurs due to social distancing and other government interventions, the death rate will double each week for another two weeks.
  • Acceleration of death rates is still occurring for the 8 countries tracked here except for China and S. Korea, who appear to have successfully contained the outbreak.
  • The above Table also shows deaths per million people, with numbers ranging from 90.6 for Italy down to 1.4 for the U.S.
  • Spain is accelerating at the rate of Italy, but delayed by 11 days. This is cause for great concern.
  • Because social distancing started in earnest about a week ago, we expect to see a de-acceleration of deaths in 1-2 weeks (which assumes that infection precedes death by 2-3 weeks; we use 3 weeks in our models).
  • The Table above gives prevalence calculated for 3 weeks ago from the cumulative deaths today assuming mortality rates in the footnote to the Table. Based on the death growth rates we then forecast prevalence today correcting for recoveries, which are assumed to be close to the 3-week-old prevalence numbers. Most troubling is Italy and Spain where we forecast an infection rate of about 1 per 60-70 people. This high density of infections will make social isolation less effective than for other countries.
  • Also shown are the reported prevalence of active cases. It can be seen that our forecasts based on reasonable assumptions are typically about a factor of 10x greater than reported, except for China and S. Korea. This indicates that lack of testing is a serious shortcoming to understanding the true extent of the epidemic and reported case values should simply be ignored as not being connected with reality. All forecasts need to be connected to hard data, namely deaths.
  • The incidence forecast similarly is a few to >10x greater than reported new cases for the same reason described in the above bullet.

The big question is whether social distancing and other government interventions are working outside of China and S. Korea. Depending on the fortitude of each nation to adhere to these strict measures we should see improvement. Turnover in new cases, due to social distancing, may already be occurring, but it won’t show up in the data for new cases because of the backlog of existing cases that have yet to be confirmed by tests. In fact, the term new cases is a misnomer because they more represent new detection of old cases. There are no reliable leading indicators or current measures to tell us whether we are succeeding. We must wait 2-3 weeks for the death statistics to show this of which we are about 1 week in for the U.S. and maybe a little more for Italy.


  • Our analysis, based on death statistics and trend analysis, provides a more realistic assessment of the scope of the COVID-19 epidemic vs. reported cases, which vastly understates the true prevalence.
  • At this time, we do not yet see any evidence of de-acceleration of deaths and therefore incidence, but it may be happening, just that we are still be 1-2 weeks too soon to see this in the death statistics.
  • The success achieved by China and S. Korea gives us hope that containment will ensue throughout most of the world.

5. How are the U.S. States Doing?

(3/22/20) Washington State has gotten control, California is making progress, but New York is concerning

The United States has the 6th largest death rate among countries in the world due to the corona virus, but how are we doing? Let me say again that deaths are a lagging indicator since these events represent infections 2-3 weeks ago. But it is the only hard data we have, so our strategy is to monitor the trend in deaths in order to extrapolate the death and the prevalence from 2-3 weeks ago to today and further into the future. The U.S. looks to be spiraling out of control in terms of accelerating number of deaths (which again reflects incidence of infections 2-3 weeks ago) and number of confirmed cases (which is meaningless because it mostly represents the amount of testing and not new cases). Let’s look at the Plots below for what we know in terms of cumulative deaths and death rates (daily) for the three most affected states, Washington, New York, and California.

These data show accelerating (increasing curves) deaths for NY and CA, but less so for WA. The equations that are fitted to the data, in order to forecast to the present and the future with regard to actual prevalence of cases (vs. reported confirmed cases), are binomial equations. This represents our upper limit for forecasting and a linear fit (not shown) represents our lower limit. The Table below summarizes death totals and rates today and what we forecast for up to 3 weeks from now. We also present a calculation of prevalence and incidence 3 weeks ago reflecting death statistics today and then calculate prevalence and incidence today.

The key observations are as follows:

  • Total deaths are calculated as the geometric mean of the low and high estimates discussed above [sqrt(low x high)]. The trend is increasing approximately linearly in WA, but accelerating significantly in NY and CA, with NY totaling about a factor of 4-5 greater than CA.
  • The margin of uncertainties for total deaths are also given in the Table and you can see they are least for WA and greatest for NY and not surprisingly increase with time into the future.
  • The calculated prevalence is significantly greater than the reported confirmed cases that we all read about. Our calculation of prevalence is based on a 1% mortality rate in NY and CA, but 3% in WA given that we know the vast majority of deaths there were for the elderly.


  • Reported confirmed cases of prevalence and incidence are misleading indicators as they represent a fraction of total and new cases.
  • WA appears to be containing their epidemic.
  • NY and CA are increasing at similar rates; however, CA is at a level of about 20-25% of NY and therefore will have an easier time containing the epidemic than NY because the probability of exposure is proportionately less.

4. No Turnover in Death Rate Yet

(3/20/20) Evidence of social distancing not yet showing up in death rates, but still too soon to tell

Today we look at the death rates per day for key hot-bed countries. The Plots below show the death rate per day for the U.S., Italy, France, Spain, Iran, and U.K., all of which are showing acceleration. Also shown are the daily death rates for China, and Korea who show evidence of taming COVID-19.

Key observations are:

  • The six aforementioned countries, including the U.S., continue to show an accelerated death rate (i.e., each day the death rate is trending up).
  • China shows a clear deceleration of death rate (i.e., each day the death rate is trending down).
  • Korea appears to trending neutral on death rate (i.e., each day is similar to the previous day).

So, let’s discuss different categories of rates, which we apply to the death rates above. The Table below shows a hypothetical relative case study for five different rate behaviors. Exponential would be the case for COVID-19 if nothing was done and every infected person infected a certain number of people who in turn infect a certain number of people. This infection rate is often referred to as R0 (e.g., for R = 3, 1 person infects 3 who infect 9 who infect 27, etc.). If some preventative measures are taken, we might expect exponential growth to slow down so we consider a binomial acceleration based on the number of cases being dependent on the square of the elapsed days. Linear is growing with every day and still not good, but at least better than the above. Constant would be achieving a R0 = 1, (i.e., 1 person infects 1 person infects 1 person) in which the infection and death rate stays constant and maybe controllable, but still not the desired outcome. Decline is what we are seeking corresponding to R0 < 1.

Based on the Plots above one can sort each country into these growth categories. Key observations are:

  • France and Spain are still in full exponential growth; this is very troubling.
  • Italy and Iran are in full acceleration, but maybe slowing down, but that may be because their numbers are already so big.
  • The U.S. and U.K are in serious acceleration somewhere between exponential and binomial growth.
  • China, if the numbers are to be believed, is in full retreat and I feel the numbers are more believable than unbelievable.
  • Korea is an example of taming their problem, but in fact they never had a problem and just got ahead of any major outbreaks. This is noted by their never actually experiencing exponential growth.

Final conclusions:

  • We should not be too alarmed at this point, since aggressive intervention in terms of quarantining and mandating social distancing really only started about a week or two ago. We expect the death rate to lag the incidence (infection) rate by about 3 weeks.
  • This model predicts that if government intervention and social response are working then we should see a noticeable deceleration of the death rate in a 1-2 week time frame.
  • It would be interesting to see how these levels of acceleration correlate with the fortitude of each country to exercise social distancing.

3. COVID-19 Prevalence and Incidence

(3/17/20) Based on the analyses described in my previous post (below) and updated to today’s latest World Health Organization (WHO) data, I can make the following estimations for three time points, 3 weeks ago, today and 3 weeks from now:

You’ll need to bear with me as I explain this.

  • Recall that I am taking cumulative and weekly rates of death to surmise the prevalence (total cases) and incidence (new cases/week) for 3 weeks ago (2/23/20). That is because I assume that anyone who dies, contracted the illness on average 3 weeks earlier.
  • So on 2/23/20, I predict that there were 8,500 people in the US with COVID-19 (assuming a 1% mortality rate). Reports would have said less than 1,000, but plenty are missed for lack of testing.
  • I then calculate the prevalence and incidence by fitting a polynomial function (n=2-4 to get a good fit) the growth rate for death (see plots below or take my word for it). The polynomial fits to the curves have uncertainty so I provide low and high estimates. The plots and functional fits (for the high estimate cases) are shown below and complement the plots I emailed on 3/14 (further below).
  • So today I predict that there are 48,000 – 130,000 cases of COVID-19 in the US. The documented number is several thousand, but again a gross under-counting, so I totally ignore those pronouncements and why I started my own modeling.
  • So the US is at a very low prevalence relative to the population of 350,000,000, however, the growth rate is quite high and accelerating, so we need to exercise social distancing.
  • I also predict total deaths (low and high estimates) for the US, WW and other countries for 3 weeks from now based on the polynomial fits.
  • China and S. Korea, if the WHO database is to be believed, have done a remarkable job of containing COVID-19.
  • Italy is by far the most scariest scenario. The death rate is accelerating, but that reflects an acceleration of the prevalence about 3 weeks ago, so we will not know how effective the aggressive government intervention is until we see a rolling off of the death rate, which as I said is about a 3 week lagging indicator.
  • Same goes for the U.S. The death rate is growing at about the same rate as Italy (75% of the total deaths in just the last week). However, that is working from low numbers in the US. High estimates for prevalence of COVID-19 are about 1/3000 for Americans, but for Italians an alarming 1/30. So we are in better shape by a factor of about100x.
  • Now there are a lot of assumptions in my model, e.g., I am not accounting for recovery, but if the growth rates are accelerating that will not take things down much.

The reason I did this modeling is because of all the suspect reporting out there about total confirmed cases, which are meaningless because of gross under-counting. Further the growth rates are more due to increased testing than to actual incidence. Further I have seen some doomsday claims of hundreds of thousands of infections in the US based on nothing but conjecture. Finally the “professional” epidemiologists and modelers are getting way to complicated using to many ill-defined variables. In fact the only statistic that matters is death. That’s usually an accurate number.

I will be following the death trends and hope we see a rolling off in the US and elsewhere in the world. If Italy gets a grip on their problem, then we can be assured that the rest of the world will be OK. Hard to say what would be considered sufficient tapering off to relax social restrictions. But if China and S. Korea are any indications it could be as soon as, but not less than, 1 month. Still I’m cautiously optimistic about the prospects for the U.S. and WW.

2. Death Statistics and Trends

(3/15/20) As I’ve expressed before, I’m not satisfied with the reporting of COVID-19. Not surprising, but also appalled at the so-called experts who either like to pontificate or like to shock the public into dooms day scenarios without doing the calculations.

I tapped into the WHO (World Health Organization) data base and downloaded some key data on excel files (I will be updating these daily). Below are plots of death rates cumulatively (linear and log) and per day (linear and log). In my previous post (below) I stated that this is the only hard data we have and a potentially important way to assess trends. If we assume this is representative of incidence upon infection (at least two weeks earlier), we can use this as a prevalence (cumulative) and incidence (daily) indicator that we can then extrapolate later (by about 2-3 weeks) to get the present-day infection numbers. Here is how I worked it up and my commentary:

  • China: If we can believe the numbers, they have radically controlled the number of outbreaks and deaths. I thought there might be state deception so I was looking for dislocations in the data that did not fit any reasonable (if not normal) distribution as a red flag to fudging the numbers; but not actually seeing that. Seems believable at this point.
  • U.S. is not in big trouble, yet. These are high growth rates, but working off of very low numbers. However, there is a definite acceleration. Will follow carefully over next few weeks.
  • WW is not super alarming but maybe pulled down by China recovery statistics.
  • Italy – This country has a huge problem. An accelerating epidemic and a case study how this could escalate to any other country. Important to find out how this got so out of hand before government intervention came into play.
  • South Korea is getting a handle on things. It is at less than 10% of Italy now and receding faster. Another example of government intervention working.

One of the conclusions for the U.S. is that the number of real infections (much greater than those confirmed by tests) is not 100x as some pundits say, but maybe 10x. How do we know? By determining the death rate for today, representing incidence two weeks ago and then extrapolating to today. Quick calculation is if 6 deaths a day today represents incidence about 3 weeks ago and if giving an upward estimate of 15 deaths/days over the next 3 weeks and a mortality rate of 1% says 420 deaths over the next 3 weeks and therefore today there must be 42,000 with COVID-19. My gut says must be more, but the numbers based on deaths seem less alarming then we are reading in the press, at least in the U.S. If it is truly more then it suggests the mortality rate may be less than 1%. So, it doesn’t matter. What really matters is the death rate and when does that start to roll over. Need at least 2 more weeks of data to get good trends.

1. COVID-19 Testing in the U.S.


The Table above shows how poorly we are doing implementing COVID-19 tests in the U.S. vs. other countries. So in the U.S. today we have about 3,000 confirmed cases and 57 deaths. The former is a leading indicator and the latter a lagging indicator, which is why you can’t divide them to get a mortality rate. All the confirmed US cases are by tests. You can see tests are administered to only 0.0005% of the U.S. population. So how to calculate the true prevalence? Generally by using the death rate and dividing by the presumed mortality rate. In that case it doesn’t look so bad if we only have 57 deaths. That would say about 5,700 cases (assuming a 1% mortality rate). But some people estimate that real cases in the US are 10-100x confirmed cases and I can’t disagree. If so there should be a lot more deaths coming up. The best metric will be death growth rate. Today there were 8 more deaths in the U.S, which would say about 800 new cases per day 2-3 weeks ago assuming death comes 2-3 weeks after infection. If I track this for a few days I can get the growth rate, which would give prevalence and incidence for 2-3 weeks ago. I can then extrapolate prevalence today based on the trend. I’m sure someone else is doing this but I can’t find anything.