C19 - quo vadis?

A small, bald headed man leans out of the balcony. He skilfully holds a large Cuban cigar in his mouth while joyfully waving to a huge and densely packed crowd of jubilant people. It is 8 May 1945. Sir Winston Leonard Spencer-Churchill is celebrating along with the masses on every city's street and square the unconditional surrender of Nazi Germany's armed forces.

75 years later, the United Kingdom is now remembering VE-Day under lockdown. Many of its streets are deserted and filled with a frozen silence. We are locked up at home, because the outcome of this pandemic is uncertain and remains contested. In fact, every new finding on COVID-19 (C19) cannot stand for evidence-based knowledge yet. But today's policy responses must rely on exactly those preliminary results from the scientific community. Consequently, governments are struggling to strike an appropriate balance between the desired policy outcomes and their negative effects on citizens' lives [1]. As such, the current political decisions will inevitably lead to "confused and hesitant" reactions. However, this is also the way of how the best science proceeds. "The science" of C19 still refers to an ongoing process. The following analysis must thus be taken with a pinch of salt, too.

Here, I'll show how a very simple model can help us in tracking the epidemic progress of nations. The method might allow for a fair comparison of the reported casualties, qualitatively. I'll reflect about some important humanitarian aspects in our fight against diseases as well.

A numbers game with the dark figures of populations

Currently, Tomas Pueyo and his team are throwing a bright light on the C19 pandemic. They concisely explain the current developments and our available options in simple terms [2-6]. In brief, it has become a numbers game. Our enemy is a respiratory virus and its overall transmission rate R is his fighting power against humankind.

As today is VE-Day, let us compare the reported number of deaths with the casualties from World War II (WW2) to better grasp the severity of the coronavirus disease. Of course, the former event lasted over a much longer time frame (six years) than the latter, which is still in its unfolding. But we could look at the daily average of casualties, i.e. the number of fatalities divided by the number of battle days:

Whilst WW2 was the deadliest conflict in history, C19 now rages through some countries with a rate already exceeding their then daily casualties. It is a devastating pandemic and we have no choice than to make time to our ally, because we cannot win this battle yet. If we buy ourselves more time, the more we can learn about the impact of our measures on reducing R along with their social and economic knock-on effects.

We should, however, emphasise that the language of war is only useful up to a certain point, because "the battle" refers to our collaborative efforts either in controlling the virus via lockdowns or in the quest for an effective vaccine. Critically infected individuals cannot battle against death for themselves. Their fate is not a fight and does not solely rest in the hands of brave health care providers (who work under immense pressure and risk). In effect, we are just beginning to understand how C19 causes disease in the first place.

In the following, I'm not attempting to replicate Pueyo's analysis in any way. I'm also not an expert in virology or epidemiology. But as a scientific researcher, I may comment on 1) the population size 2) the number of (un)reported cases, and 3) the fitting of a model to datasets.

1. From day to day we see more and more cases of C19 in the news. Although these numbers often refer to the total number of cases, different countries differ in their population size. As such, this practice can draw a misleading picture. For example, raw numbers do not always allow for a direct comparison of how different countries cope with the same epidemic. To gain a clearer grasp of how (in)effective our reaction measures are, we could quote the number of cases in reference to one million citizens, effectively adjusting for population.
2. What if all recorded cases with clinical symptoms are only the tip of an iceberg? For example, 86 percent of cases were found "undocumented" and yet responsible for most of the virus's spread in China before the restrictions came in [7]. The study showed that infected people without symptoms were the source of 79 percent of further infections, indicating that C19 is largely spread by people with barely any symptoms.
3. If we wish to study the progress of an ongoing disease, we need a model. A theoretical model enables us to change every single parameter at will, such that we can better understand their impacts on the eventual outcomes. But all analysis is only as good as the datasets, and C19 appears to wildly spread in the shadows of covert infections and widely insufficient tests. If we cannot rely on the reported numbers of infected individuals, we may turn to the reported numbers of deaths by C19. But when daily announcements only refer to deaths in hospital, as it used to be in the UK, this practice conceals the actual figures. There is also generally a delay in reporting deaths of a few days (or even longer). And, when enormous strains on the health care system are testing its collapse, we may need to count collateral cases of C19 to its death toll, too. For these reasons, theoretical models cannot fully explain our datasets, because the numbers are still deeply unreliable. Eventually, this will be possible once we can trust the reported numbers (in a few years time). But in an ongoing epidemic, epidemiologists rightly say that models are "more like a compass than a crystal ball".

What if all recorded cases with clinical symptoms are only the tip of an iceberg?

Where are we heading today?

In the following, we focus on the European countries Italy, Spain, Germany, France and the United Kingdom (UK); the United States (US) as well as China are included for comparison. We will assess their daily progresses by fitting the reported number of deaths to a very simple epidemic model while tracking the parameter developments. We first divide all data by their population in millions, so to effectively normalise the reported cases to a fraction of one million citizens.

We only focus on the reported death rates, because this allows for qualitative statements. By assuming the worst day with the greatest number of fatalities has already occurred, we may fit the open datasets (see: WorldOmeters.info) with a logistic function:

N refers to the total number of deaths by C19 amongst one million citizens at the end of the epidemic. The parameter r describes the proportional increase in the number of dying individuals per day. At the time t = tw, half of the total fatalities is recorded. It is also the moment with the greatest casualties, because the epidemic unfolds exponentially before it abates at t = tw.

Although our analysis is based on a na?ve method, this model already predicted epidemic outcomes after the day with the greatest number of new cases had passed [8, 9]. Still, as this assumption might not hold for C19, we should refrain from conclusive statements. For example, there are inconsistencies, underreporting and heterogeneity within countries. But, on the other hand, the policies adopted by different countries show very large differences in effects that would seem to dwarf such worries.

The new virus on the world stage

Even if we long for our vivid social life that we enjoyed before, we soon need to redefine "normality": No matter how we crunch the numbers, this pandemic is just getting started.

For the first wave of C19, two questions are recurring in our minds: 1) when does it get better and 2) how high will our death toll climb? Again, as our analysis relies on under-reported casualties, the following two figures only refer to the reported number of cases.

For the listed countries, the left figure identifies their critical moment, tw, whereas the right figure estimates their projected (final) death tolls, N, on a daily basis, from 30 March to 8 May 2020. France's peak at day 49 (blue curve) is due to the inclusion of data from nursing homes. At the start of the epidemic, everything is still uncertain, and we see large variations before the model parameters slowly but steadily increase; the slope thereby indicates how well our model follows the reported datasets. For example, if our model parameters keep changing from day to day, we cannot draw final conclusions. The epidemic would only ebb away if the parameters remained constant over time, because its critical moment, tw, and the total number of casualties, N, were then both well defined. In contrast, the steeper the rise, the more likely the disease is resurging again. Now, even though our simple model underestimates the real numbers, we can identify trends in how countries cope with this novel respiratory virus.

The C19 pandemic is not a competition of national health care systems. It is a global stress test of our abilities to ally against a novel respiratory virus.

Assessing the death tolls of our nations

Importantly, benchmarking countries' death tolls cannot be the focus of our attention. What would be the point of such an undertaking? As populations vary from country to country, a nation's health system is set up to meet its specific demographic needs. In addition, varying geographical landscapes, diverse socio-cultural norms and different political leaderships can greatly affect the spread of a pathogen, too. Consequently, the C19 pandemic is not a competition of national health care systems. It is a global stress test of our abilities to ally against a novel respiratory virus. We must learn from our and others' efforts and mistakes, while acknowledging the (in)effectiveness of measures in its national context. Comparing countries death tolls only becomes important in aid of global cooperation, because they indicate where the resources and capacities are needed the most in our battle against this virus.

From the previous figure, we can extract two key points. First, all the listed countries have surpassed their "critical moment". Second, this date is artificial, because the projected (final) death tolls are still increasing from day to day. For example, the critical moment appeared to occur around calendar week 7 in the US, but it then kept shifting by 5 days per week. It is now at week 9. Consequently, from the slope, i.e. by how much the critical moment shifts per week, we can (qualitatively) infer how well countries are coping with C19. Once the slope remains zero, our model parameters would finally be fixed. The following table now compares the weekly averages of the countries' slopes:

One month ago, we had overestimated the critical moment for the World, because its slope showed a negative trend. This might result from the imposed lockdowns and social distancing rules. In fact, most of the listed countries indeed reduced their slopes. China recently revised the reported numbers which causes the artificial rise.

If we interpreted the "critical moment" as the half-term of a first C19 wave, we may visualize the death tolls (controlled for population) on a normalized time axis:

The solid lines refer to our modell. They are based on the current datasets (shown as scattered dots) for the recorded deaths involving C19 and occurring between 30 March and 8 May 2020.

• The time-delayed outbreaks now overlap, because the length of the time axis (100%) refers to the projected length of each country's own C19 wave (= 2 * tw).
• We can see how far each country has progressed in the pandemic.
• A dashed vertical line marks the critical moment with the highest number of fatalities. Although all countries have passed this artificial key date, the fits keep underestimating the final death tolls. This probably reflects the difficulties each country faces in repressing the disease and its casualties.
• China's very low numbers are likely incorrect.

However, many questions can still not be answered and remain open: How well can we control the spread of C19? Is the resurgence of more casualties already the start of a subsequent wave?

Beyond C19 -- a better world is possible

“There are decades where nothing happens; and there are weeks where decades happen” are the words from Vladimir Ilyich Lenin in the context of the Bolshevik revolution. 100 years later, they cannot picture any better the situation we are currently living through, despite this global pandemic has been quite clearly predicted: Two years ago, the outbreak was a trial in the largest citizen science experiment of its kind, and the BBC even broadcasted its findings; three years ago, the national health service (NHS) failed a major cross-government test of its ability to handle a severe pandemic; five years ago, Bill Gates unmistakably rated the EBOLA epidemic as a wake up call, but we deemed his scaremongering as "too terrifying" and looked away...

In fact, how to tackle a situation riddled by anxiety and uncertainty? Today, we are shattered and buried under a tsnumai of information [2-6]. We gratefully long for guides that make sense of "a problem that is too big for any one person to fully comprehend" [10]. We want to see more progress and we desire to learn from the fall-backs, such that we can channel our powerless feelings into meaningful actions alias "dances" [4, 5].

Humblingly, we may realise that C19 will not go away anytime soon. Science, technology, engineering and mathematics can enlighten our paths into the future only up to a misty point. But whilst we are entering the global battle against an invisible enemy, we shall not forget that "crunching the numbers" and "flattening the curve" are expressions that (deliberately?) mislead us into replacing the tear of a collapsing care worker, the last breath of a fellow human being or the heartbroken pain from losing a loved one with abstract numbers and prosaic words. Do we look at the lives behind numbers? How much do we care about humanity?

Researchers have estimated that there are every year up to 4 million cases and 143,000 deaths worldwide due to cholera. These are more deaths as the ten largest countries currently register for C19 altogether (99,000). Whilst they cover half of the earth's entire land area, in Yemen alone over 5 million children are again facing the heightened threat of cholera, in this very moment. Apparently, the Third World must endure devastating epidemics: We don’t have a vaccine for tuberculosis, HIV and malaria, but we do suddenly have 100 vaccine candidates for C19 in the pipeline. Could the outbreak become another excuse of the richest countries to abdicate from their responsibilities for eliminating global inequality divides? Are we going to make sure that people in the poorest parts of the earth will not die of coronavirus in 200 years' time? As saving poor children does not lead to overpopulation, but rather the opposite, a better world is possible -- if we care enough.

References

[1] David Adam, New Scientist, Beyond the science of covid-19, 28/03/2020

[2] Tomas Pueyo, Medium, Coronavirus: Why You Must Act Now, 10/03/2020

[3] Tomas Pueyo, Medium, Coronavirus: The Hammer and the Dance, 19/03/2020

[4] Tomas Pueyo, Medium, Coronavirus: Learning How to Dance, 20/04/2020

[5] Tomas Pueyo, Medium, Coronavirus: The Basic Dance Steps Everybody Can Follow, 23/04/2020

[6] Tomas Pueyo, Medium, Coronavirus: How to Do Testing and Contact Tracing, 28/04/2020

[7] Ruiyun Li, Science, Substantial undocumented infection facilitates the rapid dissemination of novel coronavirus (SARS-CoV2), 16/03/2020

[8] Shi Zhao, Parasites & Vectors, Simple framework for real-time forecast in a data-limited situation: the Zika virus (ZIKV) outbreaks in Brazil from 2015 to 2016 as an example, 12/07/2019

[9] Wuyue Yang, medRxiv, Rational evaluation of various epidemic models based on the COVID-19 data of China, 16/03/2020

[10] Ed Yong, The Atlantic, Why the Coronavirus Is So Confusing, 29/04/2020