Update -- COVID-19 Model: Estimated Number of Infected Individuals Based on the Number of Deaths

I've had a chance to examine my model in light of evidence from South Korea that I collected from the Johns Hopkins CoronaVirus Resource Center (https://coronavirus.jhu.edu/map.html.) South Korea has clearly had one of the best if not the best COVID-19 mitigation strategy that has a centerpiece aggressive testing. Therefore, South Korea's numbers should be the most up to date and accurate.

As of 16 March 2020, South Korea's numbers are:

• 8,162 infected
• 75 deaths

Johns Hopkins doesn't breakdown the deaths by age group, however, I entered what I believe are realistic numbers into the fields. Here are the results:

Age Ranges, Years	Rate of Death	Reported Deaths	Projected Number of Infected at Present (based on average time of illness until death)	Projected number of who are infected now	Projected number of deaths based on the number currently infected (based on average time of illness until death)
80 plus	0.148	21	142	803	119
70-79	0.08	17	213	1202	96
60-69	0.036	13	361	2043	74
50-59	0.013	8	615	3481	45
40-49	0.004	7	1750	9899	40
30-39	0.002	4	2000	11314	23
20-29	0.002	4	2000	11314	23
10-19	0.002	1	500	2828	6
0-9	0.0	0	948	5360	0
Infection rate	2.0
Average time of illness until death (weeks)	2.5
Total Infected based on current number of deaths	8528
Total Infected Now	48244
Total number of deaths	75
Projected total number of deaths based on the current number of infected individuals	424

The numbers to focus on are "Total Infected based on current number of deaths" and the "Total number of deaths." I'm assuming that the total number of infected in South Korea is close to being complete. I'm estimating that South Korea has 8528 infected individuals. However, because of the lack of testing in the US, I would estimate that when the US reaches 75 deaths, that in reality there are 48244 infected. And that the US will see 424 deaths within 2.5 weeks.

I noted one flaw in my estimator. Every cell of reported deaths from 80 plus to 10-19 must have a number other than zero to achieve a reasonable number of infected estimate for that age group. I'll see if I can build in correction mechanism that would enable one to enter zero for an age group and still have a reasonable estimate of the number who are infected. 

Update: Estimate of the Number of Infected in the US Based on Current Number of Deaths (16 March 2020)

As of today, the number of COVID-19 deaths is 74. Based on that information, here's what I estimate to be the number of infected.

Age Ranges, Years	Rate of Death	Reported Deaths	Projected Number of Infected at Present (based on average time of illness until death)	Projected number of who are infected now	Projected number of deaths based on the number currently infected (based on average time of illness until death)
80 plus	0.148	21	142	803	119
70-79	0.08	17	213	1202	96
60-69	0.036	13	361	2043	74
50-59	0.013	8	615	3481	45
40-49	0.004	7	1750	9899	40
30-39	0.002	4	2000	11314	23
20-29	0.002	3	1500	8485	17
10-19	0.002	1	500	2828	6
0-9	0.0	0	885	5007	0
Infection rate	2.0
Average time of illness until death (weeks)	2.5
Total Infected based on current number of deaths	7966
Total Infected Now	45062
Total number of deaths	74
Projected total number of deaths based on the current number of infected individuals	419

I decided to use fundamentally the same distribution pattern as I estimated for South Korea. These are the results:

• The estimate for the number infected throughout the US this day is 45,062. 
• 7966 people were infected 2.5 weeks ago.
• Approximately 2.5 weeks from today (end of March, first of April) I estimate 419 people will have died from COVID-19. I suspect that's a low estimate. If 17% of those infected require hospitalization at one point or another, I suspect that many will not receive treatment because of lack of resources and personnel. And many more will die due only to the lack of treatment because of the lack of preparation. 

A Second Update Regarding the US (16 March 2020)

I just heard that the number of deaths is 80. So based on that new number, these are my estimates:

Age Ranges, Years	Rate of Death	Reported Deaths	Projected Number of Infected at Present (based on average time of illness until death)	Projected number of who are infected now	Projected number of deaths based on the number currently infected (based on average time of illness until death)
80 plus	0.148	24	162	917	136
70-79	0.08	18	225	1273	102
60-69	0.036	13	361	2043	74
50-59	0.013	10	769	4351	57
40-49	0.004	7	1750	9899	40
30-39	0.002	4	2000	11314	23
20-29	0.002	3	1500	8485	17
10-19	0.002	1	500	2828	6
0-9	0.0	0	908	5139	0
Infection rate	2.0
Average time of illness until death (weeks)	2.5
Total Infected based on current number of deaths	8176
Total Infected Now	46250
Total number of deaths	80
Projected total number of deaths based on the current number of infected individuals	453

• The estimate for the number infected throughout the US this day is 46,250.
• 8176 people were infected 2.5 weeks ago.
• Approximately 2.5 weeks from today (end of March, first of April) I estimate 453 people will have died from COVID-19. 

COVID-19 Model: Estimated Number of Infected Individuals Based on the Number of Deaths

Background

I hope this post might do the people in the US some good. I created a model to estimate the number of currently infected individuals based on the number of people who have died from COVID-19. 

My motivation for creating the model I'll discuss below originates from my feelings about the absolutely abysmal and utterly incompetent response by the Trump Administration to addressing the threat that COVID-19 posed. 

The Trump Administration had clear warnings that this pandemic was coming. In fact it's being reported that HHS Sec. Azar became alarmed weeks ago about the disease wave that was about to hit the US and Trump would not listen or direct anyone to do anything  related to preparing for the coming pandemic. I'll state here and now that this lack of response, this terrible failure is nothing short of criminal. If Trump were a military officer, he would be prosecuted for dereliction of duty. He certainly has failed the country that he took an oath to protect. 

And Trump has gall to tell everyone that he's not responsible. Or that the actions and policies that he implemented were actually implemented by someone else. Telling lies, upon lies, upon lies is the Trump way. Also Trump constantly states that nothing is his fault. Trump acts as if he's the victim and if you know Trump, that's his typical response. And unfortunately, it's a response that has gotten him out of a lot of trouble in his lying, miserable, criminal and poorly managed life. Trump is responsible, the "buck" stops with the President. All this should never be forgotten. 

As a result of Trump and rest of his sycophantic horde's inaction, the US finds itself in a terrible position with respect to understanding the progress of the spread of COVID-19 because of the failure to develop the capability for mass testing for COVID-19.  The kind of testing program that other countries found the wherewithal to develop, but the Trump Administration seems unable to do.

In response, I realized that there might be a way to estimate the current number of infected individuals based on the number of people who have died from COVID-19. 

The Model

The model is partly based on the Report of the WHO-China Joint Mission, 28 February 2020 by the World Health Organization. (https://www.who.int/docs/default-source/coronaviruse/who-china-joint-mission-on-covid-19-final-report.pdf) The study is based on 55,924 laboratory confirmed cases. What interested me from the study was death rate based on the age of the infected individuals. That information is shown below:

Age Ranges, Years	Rate of Death
80 plus	0.148
70-79	0.08
60-69	0.036
50-59	0.013
40-49	0.004
30-39	0.002
20-29	0.002
10-19	0.002
0-9	0.0

Using the information shown above allowed me to create the model you see below. I have included "dummy data" show how it operates:

Age Ranges, Years	Rate of Death	Reported Deaths	Projected Number of Infected at Present (based on average time of illness until death)	Projected number of who are infected now	Projected number of deaths based on the number currently infected (based on average time of illness until death)
80 plus	0.148	200	1351	7644	1131
70-79	0.08	50	625	3536	283
60-69	0.036	25	694	3928	141
50-59	0.013	15	1154	6527	85
40-49	0.004	6	1500	8485	34
30-39	0.002	4	2000	11314	23
20-29	0.002	2	1000	5657	11
10-19	0.002	1	500	2828	6
0-9	0.0	0	1103	6240	0
Infection rate	2.0
Average time of illness until death (weeks)	2.5
Total Infected based on current number of deaths	9928
Total Infected Now	56160
Total number of deaths	303
Projected total number of deaths based on the current number of infected individuals	1714

The number of Reported Deaths (within the age range) is variable. The number of deaths is the input. It's a simple calculation to determine the number of people who were infected when those who died were infected. However, dying from COVID-19 is not like dying from 1918-1919 influenza where you could come down with it in the morning and be dead by the end of the day. It's my understanding that it takes about on average 17 days from onset of symptoms until the person dies. That's about 2.5 weeks as shown in the model. However, in my model that is a changeable parameter. What is also changeable is the infection rate. That is, the number of people an individual will infect. In this example, I have set it to 2.0 because indications have been that the number of infected doubles each week.

Note that the death rate for children 0 to 9 is zero. There have been no reported deaths for children in this age range. That has necessitated some data fudging on my part to get what would seem to be a realistic estimate of the actual number of infected individuals. Children may not die from the virus but they are extremely effective carriers and spreaders, and need to be considered in a model that needs to estimate the number of infected individuals.

So, using the data that I have input in each age range cell (the number of reported deaths by age range), I have estimates for the number of individuals who were infected when those who died were infected. And the number of infected individuals should would be expected to be infected currently. I also estimate the number of deaths that will occur in the future, in this case 2.5 weeks from this point in time. 

One more thing, the number of infected individuals for those 0-9 is based on the average number of infected individuals from 10-19 to 80 plus. Since I'm not an epidemiologist, I considered that the average of all other groups would be the best estimate for the 0-9 age group.

For those interested in receiving a copy of this model

I created this model using Apple's Number spreadsheet. I can convert the spreadsheet to MS Excel. If you are interested in receiving a copy of this model, send me an email. My contact email address can be found at the end of "About Me." 

This is a completely new model. And I'll likely update it once more test data become available. I'll publish additional articles when I have updated and revised the model.

One more thing to note: if you use this model, I suggest inputing the total number of deaths from COVID-19.  I'll have more to say about this issue in future articles.