But is the growth of the #CoronaVirus pandemic really exponential?

By Christopher Monckton of Brenchley

Let us begin with today’s good news. The mean daily compound case-growth rates of Chinese-virus infections (Fig. 1) and of deaths (Fig. 2) continues to fall just about everywhere. It is these case-growth rates that governments chiefly use in determining how severe the control measures to manage the pandemic need to be, and how long they need to last, and whether, if they are relaxed, they can be relaxed some more or must be tightened again.

Fig. 1. Mean compound daily growth rates in confirmed cases of COVID-19 infection for the world excluding China (red) and for several individual nations averaged over the successive seven-day periods ending on all dates from March 14 to April 9, 2020. PowerPoint slides showing high-quality images are here. [Mods, please link]

It is encouraging that in all the territories studied here, the daily compound growth rate of total confirmed cases is heading downward. But the mean daily rate for the world excluding China and occupied Tibet is still 7.2%. At that rate, the 1,521,745 confirmed cases up to yesterday would become 6.5 million over the next three weeks to the end of April, and 50 million by the end of May.

It is the daily case growth rate, more than any other number, that will decide whether governments introduce, maintain, modify, end or reintroduce lockdowns. During the early phase of the pandemic, it is the crucial number that governments and epidemiologists follow, which is why the seven-day average daily case growth rates are shown in these daily graphs.

Fig. 2. Mean compound daily growth rates in reported COVID-19 deaths for the world excluding China (red) and for several individual nations averaged over the successive seven-day periods ending on all dates from March 23 to April 8, 2020.

Those who support ending all lockdowns, allowing the old and the sick to die in large numbers and risking the general population’s health by overloading the healthcare system are prone to overlook, and even to try to argue against, the salient fact of any pandemic: that in its early stages its growth is strictly exponential. One multiplies each day’s total cases by the observed growth factor to obtain the next day’s total.

That exponential growth factor will not diminish except in one of four circumstances:

1. Decisive public-health measures control its transmission. South Korea is the prime example: if one acts soon enough to identify all cases, trace their contacts and isolate all those infected the rate of spread can be contained for long enough to permit testing and intensive-care capacities to be increased in good time, and one can avoid strict lockdowns. Even then, caution is needed: Singapore, which followed much the same approach as South Korea and initially with success, has now introduced the world’s strictest lockdown, because a second wave of infection has appeared.

2. An environmental factor (such as warmer summer weather) temporarily reduces the growth rate of the infection. With a new pandemic, one may hope that warmer weather will help, but responsible governments must be prepared in case it does not.

3. There are no more susceptible people to infect, whereupon the population has either died or acquired general immunity. At the time of writing, there are 1.6 million reported cases worldwide. Suppose that there are in fact 100 times as many cases as those that have been reported (for the truth is that we do not yet know, and the reported cases could indeed understate the true rate of spread by two orders of magnitude). In that event, just 2% of the global population is infected, leaving 98% still susceptible. Even if only one case in 1000 has been reported, 80% remain uninfected. So responsible governments cannot act on the basis that general immunity has been achieved. It has not been.

4. A vaccine is found. Even then, testing it for safety takes a year to 18 months, and we still have no vaccine against the common cold.

Governments cannot responsibly sit and wait for items 2 to 4. In particular, they cannot take the risk that summer weather will do their job for them. It may, or it may not.

The most important step, where a new pathogen is spreading and is proving fatal to some, is that the public authorities should act determinedly and at the very earliest possible moment to hinder the exponential transmission that is characteristic of any pandemic in its early phase.

For those who find it difficult to get their head around exponential growth, here, plotted to scale by worldometers.info, are the daily cumulative total confirmed cases outside China and occupied Tibet for the three weeks to March 13, the day before Mr Trump declared a national emergency.

Fig. 3. Cases of COVID-19 from January 22 to March 13, 2020 (worldometers.info)

Now, was the near-20% daily compound growth in reported cases over that period strictly exponential? Let us provide a visual demonstration. Fig. 3, showing cases in thousands, shows the graph derived from the exponential-growth equation shown on the slide. The equation is derived from the numbers of confirmed cases on January 22 and March 13, and the daily number of cases is then obtained from the equation and plotted:

Fig. 4. Cases of COVID-19 from January 22 to March 13, 2020 (calculated)

Figs. 3 and 4 are scaled and drawn to the same aspect ratio. The blue borders of the two graphs will align neatly with the edges of 16 x 9 PowerPoint slides. Download today’s slide-set from the link in the caption to Fig. 1. Now you can use a technique originally developed by astronomers to find moving satellites or planets in successive images of a field of fixed stars: the blink comparator. PowerPoint is a superlative blink comparator. Go to display mode and flick rapidly backwards and forwards between slides 3 and 4.

You will at once see just how very close, at all points, the curve of the actual, real-world data plotted to scale in Fig. 3 is to the idealized exponential-growth curve calculated and plotted in Fig. 4.

Information presented like this that is useful when briefing public authorities to show them that, based on the data, the case growth rate during the early stages of this pandemic, like that of any pandemic, is necessarily and quite strictly exponential.

For no small part of the spy’s dilemma that I discussed yesterday – how an agent in the field with no specialist knowledge can find ways of reaching the truth so as to give sound intelligence to his superiors – involves assessing the available data, weighing its reliability, verifying it, cross-referencing it with other available data or known information, working out what it means and, no less importantly, presenting the conclusions in a form that the politicians will be able to appreciate, and on the basis of which they can take sound decisions.

Governments cannot afford to act on any assumption other than that the daily rate at which the total cases will grow is likely to continue on the exponential-growth curve for a month or two yet unless one of the reasons 1-4 discussed earlier comes into play.

Why does exponential growth occur during the early stages of a pandemic? The reason is that each infected person will, roughly speaking, pass the infection on to the same number of uninfected people, who will, roughly speaking, acquire or resist the infection to the same degree, and pass it on in their turn to approximately the same number of people each.

I shall end today’s posting by briefly considering the situation in Sweden, which has not imposed a strict lockdown and yet shows much the same case growth rate as countries that have imposed lockdowns. In fact, Sweden is currently coincident with the global mean.

It is tempting to assume that because Sweden got away without lockdowns we could have gotten away without them too. This is where the dispassionate advisor will think very carefully. Herb Mayer, the deputy director (intelligence) of the CIA, with whom I worked during my time with HM Government, used to say that 99% of the work of any intelligence officer, and of his agency, is handling, storing, assessing, cross-indexing, processing and, above all, thinking about information hard and dispassionately, regardless of one’s own opinion.

How might the Chief of the Joint Intelligence Committee (whose office was just along the corridor from mine at 10 Downing Street) advise HM Government, which would very much like to bring the current lockdown to an end, about why Sweden has (so far, at any rate) gotten away without the economically-crippling lockdowns Britain has adopted?

One clue – again using a visual aid – is the difference between the population densities of the major cities. Here is Stockholm from the air: low-rise, and low-density.

And here is London from the air: high-rise, and very high density.

The rate at which an infection transmits is the product of two vital quantities: the infectiousness of the pathogen and the average number of people an infected person can be expected to meet over a given time.

That is why those in London and New York who have modelled the spread of the Chinese virus recommended lockdowns: the populations there are dense enough to ensure a very much higher mean contact rate, and thus compound rate of transmission, than in Stockholm.

And that is why one cannot point to the lack of a lockdown in Stockholm and deduce that, therefore, no lockdowns were or are needed in cities where far larger populations are crammed in and piled high at far greater population densities.

The UN’s Agenda 2030 policy of cramming everyone into ever-more-densely-packed cities is a recipe for disaster in any pandemic. It is asking for trouble. We are going to have to make sure that the environmental extremists who have until now dominated policymaking among innumerate governments are no longer heeded in this as in many other respects.

Today’s sudden Singapore lockdown is a warning that, even when our own lockdowns end, they must be ended cautiously, or a second wave of infection will emerge. In Singapore, which resisted lockdown but has now been compelled by events to introduce it, any breach of the stay-indoors, keep-your-distance rules incur a fine of $10,000 and/or six months in prison for a first offense, and double those values for a second offense. Several thousand citizens were given police warnings on the first day of the lockdown.

I shall end today’s update with an image from the European mortality monitoring agency. It shows excess mortality in various European countries for the past week. It gives the lie to the suggestions made by some commenters here that there will be no excess mortality from the current pandemic. As ever, keep safe. On the data, it is those who take more precautions than the rest who are more likely to survive the pandemic unscathed.

Fig. 5. Excess mortality in England, France, Spain, Switzerland, Italy and the Netherlands for the 14^th week of 2020.

Ø So as not to make this website too coronacentric, I shall be providing the graphs of case-growth and death-growth rates daily, but shall only write these commentaries with additional information twice a week.

Link to PPTX file of diagrams.