##### April 20, 2020

Read the Reflection, written 17 August 2021, below the following original Transmission.

Is there a principled way of calculating the burden of disease on the economics of a nation? And doing so when the quality of information is heterogenous and our knowledge of the disease improves from one moment to the next? The great economist John Maynard Keynes in a letter of 1938 wrote, “The object of a model is to segregate the semi-permanent or relatively constant factors from those which are transitory or fluctuating so as to develop a logical way of thinking about the latter, and of understanding the time sequences to which they give rise in particular cases.”

In the spirit of Keynes, it’s an instructive exercise to quantitatively estimate the impact of COVID-19 hospitalizations and deaths by using simple common-sense estimates. Where these estimates make use of more or less constant factors (in this case, national death rates and the costs of medical care) in order to best estimate factors about which we know far less, or, as Keynes put it, transitory factors (in this case, COVID-19 hospitalizations and costs).

Let’s consider the case of Italy. For this country, the current life expectancy is 82.8 years.1 This number translates to one person dying every 30,222 days, or a death rate of 1/27,375 ≈ 0.0000331 people per day. Equivalently, the death rate is 0.0121 per year, or 12.1 deaths per year per 1,000 people. This naive estimate is reasonably close to the currently documented value of 10.6 annual deaths per 1,000 people in Italy.2 Using this documented death rate and ≈ 60,000,000 for the population of Italy,3 roughly 2,200 people die in Italy each day from all causes. In recent years, the leading causes of death were ischemic heart diseases, cerebrovascular diseases, and other heart diseases; these accounted for nearly 30 percent of all deaths.

The number of COVID-19 deaths in the past few weeks in Italy have been:

Daily and total COVID-19 deaths in Italy4
Date Daily Deaths Total Deaths
3/16 349 2,158
3/17 344 2,503
3/18 475 2,978
3/19 427 3,404
3/20 627 4,023
3/21 793 4,825
3/22 651 5,476
3/23 601 6,077
3/24 743 6,820
3/25 683 7,503
3/26 712 8,125
3/27 919 9,134
3/28 889 10,023
3/29 756 10,779
3/30 812 11,591
3/31 837 12,428
4/1 727 13,155
4/2 760 13,915
4/3 766 14,681
4/4 681 15,362
4/5 525 15,887
4/6 636 16,523
4/7 604 17,127
4/8 542 17,669
4/9 610 18,279
4/10 570 18,849
4/11 619 19,469
4/12 431 19,899
4/13 566 20,465
4/14 602 21,067
4/15 578 21,645
4/16 525 22,170

The peak value of the daily number of deaths in Italy due to COVID-19 (at the end of March) represents an additional ≈ 35 percent on top of the total number of 2,200 daily deaths.

Let’s use the above numbers to get a sense of the impact of the epidemic on hospitals and on the economy. For COVID-19, presumably a substantial fraction of patient deaths occur in an acute hospital setting, such as an intensive care unit (ICU). It also seems reasonable to assume that almost all patients who die from COVID-19 spend time in the ICU before expiring. In the USA, roughly 3,000,000 people die each year,5 with roughly 700,000 in-hospital deaths6 and approximately 500,000 of these deaths (≈ 17 percent) in an ICU.7

Corresponding data for Italy does not appear to be available, but it is a reasonable  assumption to use the same fractions for Italy; roughly 1/4 of all deaths occur in a hospital and roughly 1/6 of all deaths occur in the ICU. If we accept these fractions, then roughly 350 Italians die in ICUs daily. Over the nearly one-month period when the epidemic has been at its peak, the number of daily deaths in ICUs due to COVID-19 is at least 2.5 times larger than the steady-state number of 350. The stress on hospital staff who are working in an ICU setting during this peak epidemic time is hard to imagine.

The monetary costs of COVID-19 medical care are significant. Using the current number of deaths in Italy (≈ 22,000) and assuming another factor of two for patients who were gravely ill but survived,8 there are roughly 44,000 patients who have needed or are currently needing ICU care. Multiple sources indicate that the typical length of stay of a COVID-19 patient in an ICU is around 10 days.9 Multiplying by the daily Italian ICU cost of roughly $1,60010 gives an estimate of$700 million over the past month to tend to critically ill patients. It is difficult to obtain reliable numbers for the total cost of COVID-19-related medical care during the peak of the epidemic, but it is not unreasonable to make the guesstimate that the total cost is three times larger than the critical care cost. This gives an estimated direct medical cost of ≈ $2 billion which has been incurred over a period of approximately one month. The GDP of Italy in 2019 was roughly$2 trillion,11 which converts to roughly $166 billion per month. Thus, these direct medical costs represent a bit more than 1 percent of Italy’s GDP for the past month. To give some perspective, let’s translate these numbers to the scale of the U.S. In 2019, the GDP of the U.S. was roughly$21 trillion.12 An expenditure of roughly 1 percent of the U.S. GDP per month corresponds to approximately $17 billion dollars per month. This is a substantial spending rate; for comparison, the annual budget of the National Science Foundation (NSF) is$7.8 billion.13 That is, Italian COVID-19 medical costs, when scaled to the size of the U.S., corresponds to two annual NSF budgets being spent in a single month.

Another perspective comes from comparing COVID-19 medical costs with total medical costs. For Italy, health-care spending is roughly $3,000 per person annually or$250 per person monthly.14 The $2 billion estimate for acute-care COVID-19 spending corresponds to an expenditure of roughly$33 per person over the past month. Thus, the direct costs of acute COVID-19 care represent an additional 13 percent charge to the medical costs for every person in Italy; the final cost will clearly be much higher.

By using estimates about which we can be fairly certain to make projections into domains of high uncertainty, this Transmission provides a quantitative way to think about the impact of the COVID-19 epidemic on Italy.

Sidney Redner
Santa Fe Institute

REFERENCES

T-018 (Redner) PDF

Listen to SFI President David Krakauer discuss this Transmission in episode 30 of our Complexity Podcast.

## Reflection

August 17, 2021

### Modeling the Pandemic: Hindsight is 2020

I based my Transmission essay about the folly of forecasting the course of the COVID-19 pandemic on an idealized but necessarily unrealistic model for the epidemic dynamics: random multiplication. Briefly stated, the model had two elements. In the early stage, there is no mitigation and the number of new infections grows exponentially with time. When the number of infections reaches a threshold where a societal alarm occurs, mitigation is imposed that gradually, but with some fits and starts, reduces the reproduction number R0 to below 1. Reaching this point defines the end of the pandemic. The outcome of this toy model is that, although the time to extinguish the epidemic does not show much variance for different realizations of the pandemic, the ultimate size of the outbreak could vary by many orders of magnitude! This striking result suggests that forecasting the number of casualties over the course of an epidemic could be next to useless because this number is exquisitely sensitive to the details of the mitigation. The model also shows that early mitigation is crucial to reducing the outbreak size.

My essay was both prescient and quite misguided.

It was prescient because we are now witnessing the impossibility of making any quantitative predictions about the course of the epidemic. While sophisticated epidemiological models for the dynamics of the pandemic have been developed over the past year, essentially all of them have failed to account for the “unknown unknowns.” Although we have long been aware that viruses mutate, we don’t know how to incorporate their role in the COVID-19 pandemic. Will new mutations transmit more effectively or less effectively? Are they more virulent or less virulent? Which age groups are more affected? How effective will the antibodies from current vaccinations be against new mutations? How similar or different are the symptoms of the new variants? What other unknown unknowns might be lurking in the future?

My essay was also misguided because it did not account for many of the social behaviors that I couldn’t have envisioned at the start of the pandemic. One lesson that I’ve come to learn, based both on this essay and on my experience over the past eighteen months, is to simply not trust any mathematical models that are based on mechanistic differential movement of fractions of people between various health categories (Susceptible, Exposed, Infected, Recovered, Dead, etc.) according to models of the SIR type. Much more careful modeling is needed that also accounts for behavioral features more faithfully. For example, models would need to account for anti-social behaviors, such as deliberately breaking quarantine and worse.

Another aspect that I never could have imagined is the virulence (pun intended) of the anti-vax movement. While anti-vaccine sentiment has been around ever since the time that Edward Jenner invented a vaccine against smallpox, it’s hard for me as a scientist to observe how it mutated into a toxic movement that has attracted such a large following. As someone who believes that science can solve many problems, it is disheartening to see the birth of a subculture in which ignorance is celebrated and alleged individual freedom infringes on the rights of the population as a whole.

Read more thoughts on the COVID-19 pandemic from complex-systems researchers in The Complex Alternative, published by SFI Press.