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.

Death from Despair Part 4: Analysis by Age Groups

This data was collected from CDC's Wonder database for all the years available: 1999 to 2018. They're broken down into 10 year age groups from 15 to 85 (plus) years old. I removed from the figures the age groups for everyone under 15 years old and all those where the age the person was not reported. The under 15 years old age group data showed crude rates of less than 1 death per 100,000, too low to be included in the figures.

Deaths from Despair by Age Group

The figure below shows the crude rates of death from despair by age group. The dashed line curve is the overall total for all age groups to provide a baseline of comparison and a dividing line for those over, under and on the line. 

As seen in other studies two age groups, 45-54 and 55-64, show the highest growth rate  as well as the highest number of deaths from despair. Those in the 65-74 age group closely follow the Total line.   

I inserted the figure above to call attention to something that I found particularly disturbing. The age groups I have boxed are those ages that could only be considered "the prime of life." One would consider these to be the best years of anyone's life. (I know I do.) Yet in recent years, the rate of death from despair are 1) above the Total baseline and 2) the highest of all the age groups. Furthermore, the growth rates for the 25-34 and 35-44 age groups has noticeably jumped over the last 5 years.

The two age groups with little or no growth are the 75-84 and 85+ groups. Furthermore, they're below the baseline. 

The 15-24 age group has the lowest crude rate, but it's a crude rate has nearly doubled during this 20 year period and that is concerning.

Finally, to point out that during 1999, the data points for most of the age groups were in a much closer range (from 13.9 to 43.0) than in later years where the spread has become much wider from a crude rate of 25.8 to 82.1. 

Washington Post: Live updates: Coronavirus was probably spreading for six weeks in Washington state, study says; first deaths confirmed in U.S., Australia and Thailand

This just came to my attention. Here's the link: https://www.washingtonpost.com/world/2020/03/01/coronavirus-live-updates/

I expect that this article will be periodically updated.

COVID-19 Spread: Updates from the Washington Post - Updated

When a novel virus spreads, it's important to have access to trusted sources of information. Here's an article from the Washington Post regarding the spread of the COVID-19 virus around the world. This article will be updated from time to time.

Here's the link: https://www.washingtonpost.com/world/2020/01/22/mapping-spread-new-coronavirus/?arc404=true

One more thing ... if you take a look at the end of the article, there's a table of history of various diseases. One of the things that I did, was from the data provided to determine the death rate of COVID-19. Using the reported numbers, the death rate is 3.46%. (86013 inflected and 2977 deaths.) That could be high because not all COVID-19 cases are likely to have been detected. 

I updated the parameters in my quick model to 1) number of persons that an infected person would infect = 2 and 2) death rate = .0346. Number for multiple generational points = 75. 

This is what the model produced:

Generation	0	1	2	3	4	5	6	7	8	9	10	11
Number infected in Generation	1	2	4	8	16	32	64	128	256	512	1,024	2,048
Running total infected	1	3	7	15	31	63	127	255	511	1,023	2,047	4,095
Total deaths	0	0	0	1	1	2	4	9	18	35	71	142
Multiple Origination Points Infected	75	150	300	600	1,200	2,400	4,800	9,600	19,200	38,400	76,800	153,600
Running total infected	75	225	525	1,125	2,325	4,725	9,525	19,125	38,325	76,725	153,525	307,125
Total deaths	3	8	18	39	80	163	330	662	1,326	2,655	5,312	10,627

UPDATE: Of note, I reported the COVID-19 death rate as 3.46% based on the numbers supplied by the Washington Post in the article shown above. I reported that value as a death rate with caveats. However, about a week after I stated the above COVID-19 death rate, the World Health Organization (WHO) reported a death rate of 3.4%. I was about to alter my death rate to 1% based on recent reporting. But for now I'm not going to update what my model has predicted with respect to the number of deaths until I receive an updated number from WHO or the CDC.

Changing the number for multiple generational points to 42, here's what you get:

Generation	0	1	2	3	4	5	6	7	8	9	10	11
Number infected in Generation	1	2	4	8	16	32	64	128	256	512	1,024	2,048
Running total infected	1	3	7	15	31	63	127	255	511	1,023	2,047	4,095
Total deaths	0	0	0	1	1	2	4	9	18	35	71	142
Multiple Origination Points Infected	42	84	168	336	672	1,344	2,688	5,376	10,752	21,504	43,008	86,016
Running total infected	42	126	294	630	1,302	2,646	5,334	10,710	21,462	42,966	85,974	171,990
Total deaths	1	4	10	22	45	92	185	371	743	1,487	2,975	5,951

So based on the assumptions embedded in the model (and these are speculative assumptions ... please note that fact) the current state of spread of and the number of deaths from the COVID-19 virus has 42 points of origination, spread over 10 generations where the person-to-person infection rate is 2.0 and the death rate is .0346. 

This also suggests that the spread to the next generation could result in a substantial jump in the number of cases (5 figures to 6 figures) as well as well as in the number deaths. But as with all things monitoring the data and updating the model with the new data is essential.

Update

From NBC News, I received a new person-to-person infection rate and the seemingly minor change makes a pretty significant change in the numbers. Here are the parameters: 1) person-to-person infection rate = 2.2, 2) death rate remains at .0346 and the number of origination points = 39 (to match up with current data). Here's the table:

Generation	0	1	2	3	4	5	6	7	8	9	10	11
Number infected in Generation	1	2	5	11	23	52	113	249	549	1,207	2,656	5,843
Running total infected	1	3	8	19	42	94	207	456	1,005	2,212	4,868	10,712
Total deaths	0	0	0	1	1	3	7	16	35	77	168	371
Multiple Origination Points Infected	39	86	189	415	914	2,010	4,422	9,728	21,402	47,083	103,584	227,884
Running total infected	39	125	314	729	1,642	3,652	8,074	17,802	39,204	86,287	189,871	417,755
Total deaths	1	4	11	25	57	126	279	616	1,356	2,986	6,570	14,454

To reach the current number of reported infected people with 39 originating people is the 9th generation as opposed to the 10th generation. Also the jump in numbers to the next generation suggest that approximately 18,000 more people will be infected than in the previous table. 

The point I want to make is that even a slight uptick in the infection rate can have significant consequences.  This is why testing is so important. Keeping the infection rate down makes the epidemic more manageable. This is why informing the public regarding what they should be doing to not become or lower the chances of being infected is so important. This is why having competent people managing this public health emergency is so important. 

The Trump Administration

However, it seems that at the level of the Trump Administration, we have people who have no idea of what to do. Who have been denial for weeks about the likely spread of the virus outside of China and into the US. Trump's recent decision to restrict travel to and from Iran, Italy and South Korea in addition to China is not only short sighted, but utterly inane. The virus is in the US, it is spreading in the US. It's too late for travel restrictions to have any real effect. And besides, travel restrictions only buy you time to prepare, something the Trump Administration neglected to do in it's state of denial about how the virus could spread to the US.