Covid-19 Coronavirus

Looking for great info on the Covid-19 pandemic? Then LOOK ELSEWHERE because this page is getting less and less attention and is mostly out of date now. I'm writing this on 15 January 2021 - vaccinations have been going on for a few weeks now and I expect mortality in some countries to start falling in a month or two, and in other countries over the coming months, as the vaccines starts to work their magic. The biggest worry is the possibility of a variant appearing for which the vaccine is ineffective, at which point I suppose we will have to start developing new vaccines for that variant.

I made this page around March 1 2020 because mainstream media didn't seem to be giving enough attention to what I thought were essential concepts: exponential change, logarithmic graphs and doubling times. At last a mainstream medium, the BBC, has published a great article that focuses on all these things, as well as this good video (March 31). That article, as well as the BBC's coronavirus news forum and regular checks on the wonderful charts from the Financial Times, make a better and more trustworthy information base than my page, so from March 28 onwards this page will not be updated much on the assumption that you will look elsewhere.

On March 4, when there were only about 10 thousand confirmed cases outside China, I predicted on this page, based on the exponential progression of the disease outside China, that 'If that trend were to continue then we would have 461 thousand cases outside China by April 1'. That number was reached on March 27, 5 days earlier than I predicted (after 23 days rather than 28). I'm guessing that that is one of the more accurate long-term predictions of Covid-19 progression over that timeframe.

Here is some information and links to resources that will help you better understand the SARS-CoV-2 coronavirus and the Covid-19 disease that it causes. The highly-transmissible virus that has been spreading rapidly since it first jumped from animals to humans, perhaps around December 2019. If you're looking for reassurance regarding the virus then LEAVE THIS PAGE NOW for the situation is probably much worse than you think.

In fact the number of deaths increased very steadily between about May 1 and November 7 2020, with about 4500-6000 deaths per day. Then (due to winter approaching and people spending more time indoors in close proximity?) there is a second linear region, but it's steeper, meaning more deaths per day. Get the latest graph HERE.

The situation is evolving rapidly and this page should be ignored if it has not been updated within the last few days - it was last updated on January 15, 2021. Updates are integrated into the page and also listed on this page. Of course, I am not an expert and there are many pages out there written by people better qualified than me, but I think my page had something to add in the early weeks of the pandemic since the exponential nature of the spread outside China was getting little attention then.

For many days Italy was the state with the highest infection rate in the world relative to population size. You can follow this poorly reported but important metric on this page by clicking twice on the heading 'Tot Cases/1M pop'. As of March 21, Italy is now falling in the ranking, overtaken mainly by tiny states like San Marino and the Vatican where just one or two cases will push these states way up the ranking (Vatican City only has one case of March 21). These small states should really be ignored to get a meaningful ranking, in which we see that as of April 29 Belgium has the highest per capita death rate.

As of June 28, when the total number of deaths with Covid passed 500 thousand, the number of daily new deaths has been extremely stable since the beginning of May at about 4500 per day.

The Covid-19 virus jumped from an animal (probably a live wild animal) to humans in a wet market in Wuhan, China in late 2019. (Some people think that the virus may have been created in a lab, but scientists don't accept this.) In Asia there is a tradition of live animals being sold in markets, and that makes it rather easy for viruses to jump from animals to humans. Often the viruses start off in bats since bats have an unusual immune system and tend to carry lots of nasty viruses. Then the virus passes to some other animal such as a civet cat or camel, and then the virus is passed to humans. One might think that a good way to stop viruses passing to humans would therefore be to ban the selling of live animals in markets (especially wild animals) but there is a feeling that if governments tried to do this then the selling of live animals would just continue underground, making it more difficult to monitor and control. Update March 13: this Feb 24 article says 'China announced on Monday it will ban the consumption of most wild animals and severely crack down on the illegal wildlife trade to help prevent zoonotic disease outbreaks like the new coronavirus.' Good! But according to recent news reports, some wildlife markets in southern China have reopened amid the pandemic, selling dogs, cats, bats, lizards and scorpions among other species. Many Chinese continue to believe in the health benefits of consuming meat from wild animals. Two leading Hong Kong microbiologists last month condemned the continuing practice of consuming wild game, warning that “Sars 3.0” could materialise if people do not refrain from eating wild animals.

Watch this video called 'Coronavirus Pandemic' but which could just as well be called 'Revenge of the pangolins' or 'Bangkok: the next Wuhan?:

This article suggests that we can blame factory farming for the coronavirus outbreak. In the 1991s there was a push to industrialise farming in China and smallholding farmers were undercut and pushed out of the livestock industry. Searching for a new way to earn a living, some of them turned to farming “wild” species that had previously been eaten for subsistence only. Wild food was formalised as a sector, and was increasingly branded as a luxury product. But the smallholders weren’t only pushed out economically. As industrial farming concerns took up more and more land, these small-scale farmers were pushed out geographically too – closer to uncultivable zones. Closer to the edge of the forest, that is, where bats and the viruses that infect them lurk. An April 21 Guardian article says that factory farms are breeding grounds for pandemics.

We already live with a number of viruses in our environment including the flu (influenza) virus and a about half a dozen coronaviruses including the common cold virus. So why are we so concerned about the new Covid-19 coronavirus? Mainly because it is indeed a new virus and therefore humans have no immunity to it. Also, unlike the original SARS virus which made people very sick very quickly, before they could pass on the virus to many other people, the new virus often causes only mild symptoms (or none at all), making it more likely that sufferers will not be isolated and will pass on the virus to many others. Ultimately, though, the long term impact is going to be more financial than deadly, with vast numbers of unemployed and huge amounts of debt accumulating. On April 29 the International Labour Organisation warned that about half of all workers worldwide are in danger of having their livelihoods destroyed because of the pandemic, The figure equates to more than 1.5 billion people.

What we know about the virus

For a more up-to-date overview than you will find on this page, check out this Guardian article (April 12).
Most people who get the virus (about 80%) will suffer mild symptoms or none at all, about 15% will suffer serious symptoms requiring hospitalisation and about 5% will suffer critical, life-threatening symptoms.
As of late March, we think the overall mortality rate may be between 0.5% and 1%. These percentages are lower than those announced previously, based on an estimation of the total number of infections rather than just those that have been detected. Earlier in March we thought the mortality rate was about 2% overall (but, as of March 6, the WHO estimated the mortality rate to be much higher, at 3.4%). Update March 26: the chart below is from here, based on a study by Imperial College. The chart on death rates and underlying health is from the same page. This page (April 3) has an in-depth discussion of why the mortality rates seem to differ so much from country to country. Update April 29: a third of patients hospitalised with the Covid-19 virus in the UK have died, according to a study. This is very frightening news, for that's the same as for Ebola.
This April 29 article says that children under 10 cannot usually catch the virus because they do not have the necessary receptors and even if they do catch it it is very unlikely that they will pass it on.
This page (April 1) says that the mortality rate for teenagers is just 0.006% - in other words one out of every 15,000 infections among this age group will not survive. This is equivalent to saying that if a teenager catches the virus then his life expectancy decreases by about two days, but that's a bit misleading since it makes it look like all teens would die two days earlier than they would have otherwise whereas in fact it means one teen in 15000 will die within weeks of getting the virus whereas the others will live their normal lifetimes. If the mortality rate for people in their 60s is 2%, as shown in the graphic below, and if we assume that they have 25 years left to live on average, then catching the virus means a loss in remaining life expectancy of 2% x 25 years = 6 months.

Men are much more likely (about 60% more) to die from the disease than women, See the chart above for the UK, published on April 29.
People with preexisting conditions such as cardiovascular disease are also at much increased risk (see the chart above).
Statistician David Spiegelhalter has been looking into the Imperial College data and made an interesting conclusion: if you contract coronavirus, you've got the same risk of dying over the next couple of weeks as you would normally have of dying over the next year - regardless of your age and your background health i.e. the coronavirus risk of death by age chart matches the everyday disk of death by age. I interpret that as meaning that if a person catches the virus then their risk of death within the next year would be double the normal rate. And if half the people are going to get it, as Imperial College predicts (I think) then a person's risk of death would be increased by 50% for that year over the normal value. Put another way, you are twice as likely to die in the coming year from something unrelated to the virus as you are to die from the virus. I'm assuming that all the people who are going to die from the virus are going to do so within the next year, since we can hope that a vaccine will be ready around then. I'm also assuming that it is okay to add the risks of death, which is probably valid for younger people but less so for older people. My math was confirmed on April 21 when I read that currently a third of deaths are being caused by Covid-19.
Sorry to have to remind you, but when hospitals become overwhelmed, these mortality rates, especially for older people, can only rise.
What is the incubation time (the time between catching the virus and experiencing symptoms)? It is thought to be up to about two weeks. Update March 21: I just read that the incubation time is 5-6 days for 'older people' and 7 days for 'younger people'. A Lancet report gave so what longer incubation times: a median time of 10 days and a maximum of 14. People who die from the virus tend to do so within 2 to 8 weeks of first showing symptoms. This graphic from the Telegraph (April 1) seems to show an incubation time of just two days. Note that it says that you are unlikely to be infecting others from about twelve days after getting infected.

What is the average reproductive rate, R, which is the average number of people infected per case? (R0 is the average number infected per case in the absence of protective measures and immunity). If R is greater than one than the daily number of new cases will increase. If R is less than one than the daily number of new cases will decrease. R0 is thought to be about 3 for the Covid-19 virus but as of May 10 many countries have brought R below 1 with strict lockdown measures. We can reduce R by discouraging people from gathering indoors in large numbers. If we can reduce the figure to less than 1 then that means that we should be able to limit the spread of the disease. The graph below (from here) shows R0 plotted against fatality rate (as a percentage). You can see that the coronavirus appears at the first estimate to be less contagious or deadly than many others, giving hope for containment. The BBC has an article 'Coronavirus R: Is this the crucial number?'

We don't know whether the virus will mutate into something more deadly although it is reassuring to know that coronaviruses tend to mutate much more slowly than the seasonal flu virus. UPDATE: This Telegraph article says that the initial form of the virus, called type 'S' (think 'start') has mutated into a form known as type 'L' (think 'later') which is more aggressive, more infectious and more quickly spreads. Then the article contradicts itself by saying that (at least in China) "it appeared the less dangerous ‘S-type’ was now taking over, possibly because of aggressive public health lockdown measures in China, which had stopped the more virulent disease in its tracks." We don't know whether a vaccine that is effective against one strain will also be effective against the other, but it should be since the drug companies are targeting parts of the virus that are common to both strains. Update April 10: a premium article in the Telegraph says there are three main variants: the original Chinese variant, type A, a variant B and a variant C which came from B. (The article doesn't make it clear how ABC relates to S and L). Interestingly, there seems to very little type A in the UK, meaning that the virus did not come to the UK directly from China, but probably from Singapore, S Korea or Hong Kong. I suppose some strains are more aggressive than others, so if type C is particularly aggressive and type A milder than might explain the Chinese 'miracle' and the heavy impact in the UK. (the report wasn't written by Imperial). If it's true that type A is milder, might it make sense to deliberately self-infect with that type to avoid getting the much worse type C?
We don't know whether the virus is airborne, meaning that it can pass easily through the air from one person to another. The evidence so far seem to be that this virus is not airborne. When you cough, you produce up 3000 droplets but all but the tiniest of these will tend to settle to the floor quite quickly. See this July 8 article from which this is a quote 'For months, the WHO has insisted that Covid-19 is transmitted via droplets emitted when people cough or sneeze. Droplets that do not linger in the air, but fall onto surfaces - that's why handwashing has been identified as a key prevention measure. But 239 scientists from 32 countries don't agree: they say there is also strong evidence to suggest the virus can also spread in the air: through much tinier particles that float around for hours after people talk, or breathe out.'
We don't know how much immunity one has after recovering from the virus. We know of some people who recovered and then caught the virus again shortly afterwards, which is worrying. (It may be that they caught one strain and then the other?) Update March 17: it seems that there are always a few people who don't get have good immunity after recovering from a virus, so if some people catch the coronavirus twice that's more to do with these abnormal people rather than the coronavirus being abnormal. Update April 10: the best explanation is probably to be found in this article which says that some people fight off the virus with their 'innate' immune system, before the secondary immune system, the adaptive immune system, kicks in, the one that produces antibodies and T cells that can target a specific pathogen. Extract: While older patients produced the highest levels of neutralising antibodies, many patients had low levels and 10 did not appear to generate them at all. If the findings hold up – the study has yet to be reviewed and published – they have widespread implications. The more robust immune response from older people suggests their blood plasma may work best in trials that are assessing whether convalescent plasma infusions can help seriously ill patients overcome the virus. But the findings may frustrate efforts to manufacture an accurate antibody test for the virus if many people have low or even non-existent levels of neutralising antibodies. The work also has implications for “immunity passports”, which could allow people to return to normal life if blood tests showed they had developed immunity to the virus. Nearly 6% of the recovered patients had no neutralising antibodies, suggesting that other parts of the immune system had cleared the infection, without producing long-term immunity. A Wikipedia article says: The immune system protects organisms from infection with layered defenses of increasing specificity. In simple terms, physical barriers prevent pathogens such as bacteria and viruses from entering the organism. If a pathogen breaches these barriers, the innate immune system provides an immediate, but non-specific response. Innate immune systems are found in all plants and animals. If pathogens successfully evade the innate response, vertebrates possess a second layer of protection, the adaptive immune system, which is activated by the innate response. Here, the immune system adapts its response during an infection to improve its recognition of the pathogen. This improved response is then retained after the pathogen has been eliminated, in the form of an immunological memory, and allows the adaptive immune system to mount faster and stronger attacks each time this pathogen is encountered. See this July 8 article.
How long does the virus remains active outside the body? Update March 18: this article says 'the virus could survive in droplets for up to three hours after being coughed out into the air. Fine droplets between 1-5 micrometres in size – about 30 times smaller than the width of a human hair – can remain airborne for several hours in still air. It means that the virus circulating in unfiltered air conditioning systems will only persist for a couple of hours at the most, especially as aerosol droplets tend to settle on surfaces faster in disturbed air. This page says that the virus was still detectable on cardboard for up to 24 hours, and on plastic and steel for up to 72 hours. But it’s important to note that the amount of virus decreased rapidly over time on each of those surfaces and so the risk of infection from touching them would probably decrease over time as well.
Will the virus weaken when temperatures and humidity rise with the approach of summer? This was the case for the SARS virus and was a large part of the reason why the SARS virus killed fewer people than the Covid-19 virus has already killed. Update March 24: this BBC article says '.The spread of outbreaks of the new disease around the world seems to suggest it has a preference for cool and dry conditions'. It says that coronaviruses have an oily coating that hardens in cold conditions to protect the virus. But we really don't know. the devastating 1918 Spanish flu flourished in the summer, but that was not a coronavirus. It seems likely that the Covid-19 disease will become seasonal in the long term, like the common cold which is also caused by four different coronaviruses that we have been living with for years. Update July 5: the number of global daily deaths has been extremely constant since May 1 at about 4500 per day, with no sign of a decrease, but logically that does not mean that the hot weather is less favorable to the virus.
Can people without symptoms spread the virus? It's now very clear that infected people without symptoms CAN spread the virus, and this is exactly why this virus is so dangerous and why isolating people only once they have symptoms is not going to be effective.
Could you become infected from just a single particle of coronavirus? According to this page, there’s a certain amount of viral particle that you need to be exposed to become infected. If you just had one viral particle on your finger, it’s unlikely that you’re going to be infected. Some viruses are very potent, you only need like 10 particles to get infected, while others you [may] need millions. The fewer viral particles you’re exposed to, the less likely you’re going to get infected. That’s why the amount of virus on a surface is important.
When will we have a vaccine? It seems it will be at least another year before a vaccine becomes widely available (several candidate vaccines have already been made but it will take many months for them to be tested for safety and efficacy). The big pharmaceutical companies are usually not very interested in working on coronavirus vaccines since it takes so long to get a vaccine to market that it is likely that the virus will already be petering out by the time the vaccine is ready. Therefore the companies don't expect to be able to make much money from developing a vaccine. That's why no vaccine was ever developed for the SARS or MERS viruses, though a vaccine was developed for Ebola. Update March 16: The first trial in people of a vaccine to protect against pandemic coronavirus is starting in the US on March 16, but even if testing is successful the vaccine will not be ready for a year. See this great video:

Good news! This article says a vaccine could be ready in small quantities in just a few weeks for health workers (and the very rich, I suppose). According to this premium Telegraph article, (April 30) a Covid-19 vaccine effectiveness could be known by mid-June. Human trials began last week, and the University of Oxford team hopes a million doses could be administered from September. Several hundred Britons have been given the experimental jab, with hopes that “signals” about whether it works could emerge by mid-June. If it works a million doses could be given to the public from September.
Do we really need a vaccine? Couldn't an existing mild form of Covid-19 be used? Of the 100+ mutations of the Covid-19 virus that have been documented (as of March 25), one seems especially interesting. According to this page, 'A few SARS-CoV-2 viruses that were isolated from Singaporean COVID-19 patients are missing a stretch of genes that also disappeared from SARS-classic during the late stages of its epidemic. This change was thought to make the original virus less virulent, but it’s far too early to know whether the same applies to the new one. Indeed, why some coronaviruses are deadly and some are not is unclear. “There’s really no understanding at all of why SARS or SARS-CoV-2 are so bad but OC43 just gives you a runny nose,” Frieman says.' If I understand correctly, there is a mutated version of Covid-19 virus that gives just a runny nose but which might give immunity to the Covid-19 virus in general? If so then we don't need a vaccine - we just need to expose everyone to the Singaporean variant. I volunteer to be the first to deliberately self-contaminate with the Singapore variant, but will they let me fly from France to Singapore?
Can chloroquine or the milder hydroxychloroquine, more commonly used to treat malaria, Lupus and rheumatoid arthritis, really help treat coronavirus patients? This April 23 Guardian article seems to say that it might be helpful for milder cases but may do more harm than good for more serious cases. But a major study published on May 7 concludes that it does not work.
Does the anti-tuberculosis vaccine (BCG) protect against Covid-19? It seems that, unlike most vaccines, the BCG (anti tuberculosis) vaccine boosts the innate immune system rather than the adaptive one, and thus it protects against much more than just tuberculosis. I've read that the innate immune system 'carpet bombs' pathogens in general whereas the adaptive immune system uses 'laser-guided bombs' (antibodies) to target specific pathogens. That might explain why the BCG could be helpful against Covid-19. Anyway, here are a couple of articles from April 2020: livescience.com nytimes.com wired.co.uk
What about remdesivir, an antiviral? According to this April 16 article, A Chicago hospital treating severe Covid-19 patients with Gilead Sciences’ antiviral medicine remdesivir in a closely watched clinical trial is seeing rapid recoveries in fever and respiratory symptoms, with nearly all patients discharged in less than a week. Remdesivir was one of the first medicines identified as having the potential to impact SARS-CoV-2, the novel coronavirus that causes Covid-19, in lab tests. The entire world has been waiting for results from Gilead’s clinical trials, and positive results would likely lead to fast approvals by the Food and Drug Administration and other regulatory agencies. If safe and effective, it could become the first approved treatment against the disease. The University of Chicago Medicine recruited 125 people with Covid-19 into Gilead’s two Phase 3 clinical trials. Of those people, 113 had severe disease. All the patients have been treated with daily infusions of remdesivir. “The best news is that most of our patients have already been discharged, which is great. We’ve only had two patients perish,” said Kathleen Mullane, the University of Chicago infectious disease specialist overseeing the remdesivir studies for the hospital.
Plasma from coronavirus survivors (which contains the antibodies to fight the Covid-19 virus) has been found to help severely ill patients and there is a suggestion that it could even be given to people who do not have the virus, to protect them. This really could be a game changer, for there are already million of people who have recovered from the virus and carry the antibodies. A plasma transfusion trial will soon take place in France. May 10: Sorrento Therapeutics and Mount Sinai Health System in New York City have joined forces to develop an antibody cocktail they hope will shield against Covid-19 infection for up to two months. An antibody cocktail is not the same as a virus because it does not cause the body to start making its own antibodies, but I think it could still be a game changer if it can protect people for a couple on months. Getting an injection every couple of months until a vaccine becomes available would be a small price to pay for protection against the virus.
According to this Guardian article (April 22), French researchers are planning to test nicotine patches on coronavirus patients and frontline health workers after a study suggested smokers may be much less at risk of contracting the virus. The study at a major Paris hospital suggests a substance in tobacco – possibly nicotine – may be stopping patients who smoke from catching Covid-19. Clinical trials of nicotine patches are awaiting the approval of the country’s health authorities. “Our cross-sectional study strongly suggests that those who smoke every day are much less likely to develop a symptomatic or severe infection with Sars-CoV-2 compared with the general population,” the Pitié-Salpêtrière report authors wrote. “The effect is significant. It divides the risk by five for ambulatory patients and by four for those admitted to hospital. We rarely see this in medicine,” it added.
Is it possible that the MMR vaccine offers some protection from Covid-19? (April 23). A Cambridge university team is looking into this possibility. Lots of young people have had that vaccine and we know they rarely get serious harm from the virus.
April 27: Tocilizumab improves significantly clinical outcomes of patients with moderate or severe COVID-19 pneumonia.
A major breakthrough was announced on June 16. A cheap steroid drug called dexamethasone can greatly cut the risk of death from Covid-19. For patients on ventilators, it cut the risk of death from 40% to 28%. For patients needing oxygen, it cut the risk of death from 25% to 20%.
The drugs that could beat the coronavirus (April 26).
With so many different drugs being tested, the BBC did a summary on April 22: Coronavirus: When will we have a drug to treat it?
How air pollution exacerbates Covid-19 (April 28)
How long to recover? (April 26)
Covid 19 isn't only about the lungs. Some patients with high levels of inflammation experience blood clots or microclots in their lungs and legs, even after receiving blood-thinning medication, according to this April 23 article.
Most scientists believe that the virus passed from bats to some other animal and then to humans but some people have suggested that the virus may have leaked from a lab in Wuhan. It's certainly a remarkable coincidence that China's only high security (level 4) lab is in Wuhan, just 16 km from the seafood market where experts think the virus crossed to humans. Furthermore, there are reportedly two other labs just 280 meters from the market. Trump is interested in this idea, of course. See this April 17 BBC article 'Is there any evidence for the lab release theory?'.
Testing is important not only to find out who is infected (best done with a test that detects the virus's genetic makeup) or who has been infected and has perhaps already recovered (best detected with an antibody test that detects the antibodies that the body creates to fight the virus, beginning about 5 days after infection). On April 8 France announced that it has developed an antibody test (based on a couple of drops of blood from a pricked finger) which is at least 98.1% accurate.

The situation outside of China

The worldometer page that I linked to above has one graph that I find particularly interesting. Although daily new cases seem to be decreasing in China, the graph of total cases outside China shows a different story. How is China doing such a great job controlling the outbreak? This video offer a clue:

Here is the graph on March 28, 2020, though you should check the source page to see an up-to-date version. There is also an excellent Covid 19 tracker here.

The graph seems to show an exponential increase, meaning that the number of cases increases by a constant factor in equal times. But it's hard to tell whether the progression is really exponential by looking at a linear graph - the trick is look for a straight line on a logarithmic graph. Looking at the logarithmic graph below (pay attention to the scale on the vertical axis), you can see (as of 28 March) that as soon as the number of cases passed 100, around January 30, the graph is approximately a straight line, which confirms that the increase is approximately exponential. See this video for a more detailed analysis of the exponential growth of virus outbreaks. According to this good report in French, the exponential increase is likely to become less than exponential once 15-20% of the population has immunity, since infected people who would previously have passed on the virus to people with no immunity would often then be passing on the virus to people who are immune, and who won't get the disease. For a country like the UK, France or Italy, that percentage of the population corresponds to about 11 million people, so I won't try to make predictions as to how the numbers will evolve once that threshold has been reached.

On March 4, based on an older chart, I calculated that the number of cases outside China was then doubling every 5 days, i.e. a 'doubling time' of about 5 days. Put another way, the number of cases was increasing by a factor of 54 every month, increasing from 159 on Jan 31 to 8564 on March 1. I predicted that if that exponential trend were to continue then we would have 461 thousand cases outside China by April 1. That prediction was fairly accurate, given that we are talking about an increase by a factor of nearly 3000. That number (461 thousand) was reached on March 27, 5 days earlier than I predicted (after 23 days rather than 28). I'm guessing that that is one of the most accurate long term predictions of Covid-19 progression ever made public - can you find a more accurate one?

The doubling time could be extended if the confinement policies being adopted by most countries are successful.

Country by Country

As of March 13 I think there is enough data on individual countries for an analysis as to whether the virus is spreading exponentially or not, and, if so, what is the doubling time and what are the predictions?

Here are the logarithmic graphs for the number of cases in France and the UK as of March 13 . Recall that if the logarithmic graph shows a straight line that indicates an exponential growth. All the graphs show a roughly straight line after the number of cases has passed 100, and thus exponential growth with a measurable doubling time.

Analysis (as of March 13, updated March 22)

We know that many cases are not being detected. My analysis is based on the assumption that the percentage of cases that are being detected stays constant.

Note that one can find the log to base 2 of a number on this site calculator.com/scientific/ (they call it lg2). Note also that in 10 doubling times the number of cases is multiplied by about 1000 (2^10=1024).

France

The growth (above) was exponential from Feb 29 (100 cases) to March 11 (2281 cases), so cases increased by a factor of 23 in 11 days. Taking the log to base 2 of 23 we get that this is 4.52 doublings. Dividing 11 by 4.52 we see that the doubling time for France is about 2.43 days, i.e. the number of cases is doubling every 2.43 days. As long as the growth remains exponential, we can predict that by 4 April (10 doublings in the 24 days since March 11) there will be about 2.3 million cases. Update April 6: My prediction that there could be 2.3 million cases in France by April 4 if the exponential curve were to remain valid was way off, since the real figure was 'only' 90 thousand on April 4. Confinement seems to be working! The line in the above chart slowly began to level off, beginning around March 7.

UK

The growth was exponential from Feb 26 (13 cases) to March 11 (460 cases), so cases increased by a factor of 35.38 in 14 days. Taking the log to base 2 of 35.38 we get that this is 5.15 doublings. Dividing 14 by 5.15 we see that the doubling time for the UK is about 2.7 days, i.e. the number of cases is doubling every 2.7 days. As long as the growth remains exponential, we can predict that by 7 April (10 doublings in the 27 days since March 11) there will be about 470 thousand cases. Update April 10: the true figure for April 7 was about 55 thousand, so my prediction based on exponential growth was way off. This means that lockdown is making a difference - you can see the line in the above chart flattening a bit from about March 14, meaning the growth was no longer exponential like in the 10 days prior to that date.

The Institute of Health Metrics and Evaluation in Seattle, based at the University of Washington, is the best organisation in the world at collecting data on diseases and mapping out why we fall ill. According to this Guardian article of April 7, that organization has made a very worrying prediction for the UK, that by August the UK will have had more deaths (66 thousand) than Italy, Spain, France and Germany combined. Also disappointing that the figure is much higher than the 20 thousand deaths that the government was 'hoping for', and that's only up to August. The article doesn't explain why the UK is expected to do so much worse than those other countries. The organisation predicts a peak in the UK around 17 April, and things should be much better by the beginning of May.

Graphs from the Financial Times

The chart below (captured on June 12) of deaths per million allows you to better compare countries. Note that these are logarithmic graphs. On the same FT page you can find graphs for many other countries not shown below. The following FT chart (check the date under the graphic) shows new deaths per day (averaged over the previous week) and show that Sweden (a country that never did a strict lockdown) is, as of June 1, the country with the highest per capita death rate in the Europe. Click HERE for the most up-to-date charts.

The first graph highlights the US and selected european countries, the second highlights Russia and some South American countries which are worrying either because of the continuing rapid rise in death rate or because of their size.

Mitigate or Suppress?

An important report published by my college, Imperial College London, on March 16, is causing the UK government to change its controversial approach. This page explains that governments are faced with three choices:

Do nothing and let the virus sweep rapidly through the country. For the UK, this would leave more than 500 thousand people dead by August.
Mitigate: accept you cannot stop the coronavirus so slow its spread and prevent a massive peak in cases that would overwhelm the national health service while trying to protect those most at risk of severe disease. For the UK, this would leave 250 thousand people dead from the virus.
Suppression: use even stronger measures to break chains of transmission, effectively trying to stop the epidemic in its tracks, and bring cases down as low as possible, as China has done. For the UK, this would leave perhaps 20 thousand people dead from the virus, or rather 'with' the virus, since the figure includes people that would have died anyway. It's really a best-case number. That's about one in every 3000 people. If the same proportion were to be killed globally that would be about 2.3 million people. Since these are probably best-case numbers, I expect the real numbers to be higher.

Until now, most countries have chosen suppression, but the UK appeared to have chosen mitigation, until March 16. The report by Imperial says that the mitigation strategy is better than nothing, but would still result in about 250,000 deaths and would completely overwhelm intensive care in the NHS, with the limits of intensive care "exceeded by at least eight-fold". The report concludes "suppression is the only viable strategy at the current time". It is hoped deaths could be limited to the thousands or tens of thousands." However, the suppression approach comes with major problems. It effectively requires shutting down parts of society and there is no exit strategy. As fewer people would be infected there would be little immunity in the population and cases would soar soon after measures were lifted again. Quoting directly from the report, 'The major challenge of suppression is that this type of intensive intervention package – or something equivalently effective at reducing transmission – will need to be maintained until a vaccine becomes available (potentially 18 months or more) – given that we predict that transmission will quickly rebound if interventions are relaxed.'This is the conundrum China now faces. Research suggests 95% of people in Wuhan were still susceptible to the virus at the end of January. The report suggests we may have to wait 18 months for a vaccine, but even that is not guaranteed. We could be in this for the very long term. I still think the Ward Plan (see below) has its merits. The following chart from this page (March 21) illustrates the three options for the UK. That figure of 20 thousand is probably a best case scenario:

Wouldn't these people die anyway?

The same page states that every year more than 600 thousand people die in the UK and that the announced coronavirus deaths would not be on top of this - there would be a significant overlap i.e. many of the people dying with the coronavirus would indeed have died anyway. If half of those 20 thousand would have died anyway then the number of deaths would have been increased from 600 thousand to 610 thousand by the coronavirus, an increase of just 1.7%. I find it reassuring that the number of people that might die of coronavirus in the UK (in this best case scenario) is small compared to the normal number of deaths each year. On the other hand, 20 thousand would be much more than the number of people killed by flu each year.

Might it make sense to deliberately self-contaminate?

I wonder whether it would perhaps be logical, in some cases, to deliberately catch the virus. I'm asking this question to promote discussion, not to encourage you to actually self-contaminate. One reason to deliberately catch the virus would be to know that if you need hospital care you are more likely to get that now, before the hospitals are overwhelmed, which is starting to be the case in northern Italy. Also, if you catch the virus deliberately you will know that you have it and you can self-quarantine until recovered (assuming you do recover), therefore being confident that you will not pass the virus to anyone. People who have recovered may be immune to both strains (?) and may not (?) be carriers any more, in which case they would presumably be able to go back to work and live a fairly normal life. Deliberate self-contamination would probably make more sense for people under 40 who are almost certain to recover. On the other hand, it's people over 40 who have to worry that they may need hospital care that may soon not be available.

The Ward Plan

My non-expert analysis of the data for countries other than China suggests that each country has exponential growth with a doubling time of 2 to 5 days that we can expect to continue until 15-20% of the population is infected. Unless the draconian measures in place in some countries can break the exponential nature of the spread of the virus, or greatly extend end the doubling time, then the outbreak is likely to peak in late April or early May, according to my calculations. If about 70% of the world's population gets the virus and if the mortality rate is 3% then more than 150 million people will die, most of these being old people. We need to do everything we can to protect older people, so here's my plan (I present this plan only to promote discussion, knowing that it has no chance of being applied):

Deliberately infect everyone under 40 years of age who has no pre-existing health condition. Of course, you could not do that simultaneously for certain workers such as health workers or police since they are badly needed, but you should do it ASAP.
Keep all these people in strict quarantine until they are no longer contagious, which I assume means about two weeks. Nearly all these people should suffer no more than mild symptoms for just three days, so they could be quarantined at home. Once they recover they will have immunity.
When the quarantine ends, all these people who are currently a huge threat to old people (since they can be carriers of the virus without showing symptoms) would no longer be a great threat to them (though an immune person could of course still pass on the virus e.g. by shaking hands with a sick person and then with a healthy person). All these young people could return to work and live fairly normal lives, confident that they do not have to worry about catching and passing on the virus any more. I imagine most of the workforce is less than 40 years old, so having most of the work force back to work would help the world's economy rebound (also back in the workforce would be all the workers over 40 who have recovered). See this article from April 8 'Allow young people out of lockdown early to get country moving, say business experts'.
People in their 40s who do essential work that cannot be done at home would also be able to go back to work, protected by the 'herd effect' i.e. the fact that nearly everyone around them would not be carrying the virus. Even if people in their 40s get infected they have little chance of death.
Older people would still have to be very careful not to catch the virus which would still be very present in their age range, but they would have a much greater chance of surviving long enough for vaccines or a cure to become available.

My plan is based upon a number of assumptions:

People who are under 40 and who have no pre-existing health conditions have very little chance of being killed or handicapped by the virus. I've seen the figure of 0.2% (1 in every 500) given as the mortality rate for under 40s. (Update March 18: On French TV this evening I hear that "7% of deaths are people under 65") but I don't know whether these figures are only for France or for the whole planet. If 60% of the world's population is under 40 (a wild guess) then that mortality rate would imply nearly a million deaths among young people - I'm not going to get into a discussion about whether it is desirable to condemn to death a million young people to save the lives of tens or hundreds of millions of older people. Actually that's not a fair discussion since most young people are going to get the virus anyway and about the same number will die, it's just a question of whether they should get it early, in a controlled way with proper quarantine, of whether they should get it a bit later, without immediately knowing it (or not ever knowing it) and therefore transmitting it to many other people.
People who have recovered from the virus have little chance of catching it again and could not be carriers. This is a very big assumption - it may be, for example, that some people will not have strong immunity, or that recovering from one strain of the virus would not give you immunity to the other strain. But even in this case you could first contaminate with one strain and then, when everyone has recovered, immediately contaminate with the other strain.
I don't know what the situation is for very young children. I guess they should not be contaminated deliberately, but I don't know what the cut-off age should be.

So, Monsieur Macron, what do you think of my plan? I recognise that not everyone under 40 would agree to be deliberately infected, but under 40s could also be simply invited to self-infect, with mechanisms in place to allow that to happen. The 'corona parties' that some young Germans are organising would be an excellent way of getting young people infected. If a vast majority of under 40s took up the invitation, the results would be almost as good.

This Telegraph article (April 12) says that a leading German epidemiologist who predicted the coronavirus crisis in Europe is now calling for governments to end the lockdown and put in place a three point plan that strongly resembles the Ward Plan that I proposed a month earlier. Prof Alexander Kekulé warned the virus was about to engulf Europe and publicly urged Angela Merkel’s government to start screening international travellers as early as January. But he now believes the lockdown is in danger of going on too long and causing more damage than the virus, and has drawn up a three point plan for how it can be safely lifted:

The elderly and those with pre-existing conditions who are most vulnerable to the virus must remain in isolation.
Move from social distancing to what he calls “smart distancing”. “We need to adapt distancing to the situation. A cashier at a supermarket check-out, for instance, is going to be exposed to infection all day. He needs to wear a mask, he needs proper hygiene measures. A taxi driver needs to learn not to touch his face after handling money.”
Let the young get the virus. “People under 50 are very, very unlikely to die or get seriously ill from the coronavirus,” he says. “We have to let them get infected so they can develop immunity.”

His plan differs slightly from mine in that he says let young people contaminate one another and I say contaminate them deliberately so that they can then be put into quarantine for a couple of weeks so that they can't contaminate old people.

The Ward Plan: extensions

The essence of the Ward Plan is that since the vast majority of young people are going to catch the virus anyway (a greater proportion of young people than old people since old people are more vulnerable and will take more precautions) it makes sense to deliberately infect young people so that we know that they have it and so that they can then be strictly quarantined until they have recovered and are immune and can resume work and normal lives (only a tiny proportion will need hospitalization). The alternative is that these young people will catch the virus accidentally, and for many days will passing on the virus without necessarily experiencing any symptoms. Also, if they wait until they catch the virus than that just delays their resumption of normal lives.

Supermarkets are relatively dangerous places to be. Before you open that refrigerated cabinet, think of how many hundreds of people have touched that handle in the last day or two. The till workers are in the front line, but that's a low-skilled job that could be easily learnt by people who have achieved immunity, who will soon be very numerous, so train them to do that and replace the current till workers who are so exposed and vulnerable.

An even better solution for supermarkets is to encourage people to order online so that supermarket employees can prepare the order - all the customer then has to do is pick it up without even entering the supermarket. I'm pleased to see Carrefour in France encouraging this policy.

Retired doctors are being encouraged to go back to work, but they are vulnerable, so they should be doing consultations only by video.

Many people are not working and many students are not able to learn well since their schools are closed. Obvious thing to do: massively connect students to professionals who are not working - that would be great for both groups. Just have mechanisms in place to stop this becoming a pedophile's paradise for grooming those students.

How do we get out of this mess?

This excellent BBC article (March 20) explains that the current strategy of shutting down large parts of society is not sustainable in the long-term. The social and economic damage would be catastrophic. What countries need is an "exit strategy" - a way of lifting the restrictions and getting back to normal. But the coronavirus is not going to disappear. If you lift the restrictions that are holding the virus back, then cases will inevitably soar. "We do have a big problem in what the exit strategy is and how we get out of this," says Mark Woolhouse, a professor of infectious disease epidemiology at the University of Edinburgh. It's not just the UK, no country has an exit strategy." It is a massive scientific and societal challenge.

The article says that there are essentially three ways out of this mess.

Herd immunity by vaccination Immunise enough people, about 60% of the population, and the virus cannot cause outbreaks - the concept known as herd immunity. But the best guess is a vaccine could still be 12 to 18-months away if everything goes smoothly.
Herd immunity by infection (Enough people develop immunity through infection) The UK's short-term strategy is (was?) to drive down cases as much as possible to prevent hospitals being overwhelmed - when you run out of intensive care beds then deaths spike. Once cases are suppressed, it may allow some measures to be lifted for a while - until cases rise and another round of restrictions are needed. Little by little this approach would lead us towards herd immunity, but it could take more than two years to reach that, and we are not even sure that immunity to this virus will be long-lasting.
Permanently change our behaviour/society The third option is permanent changes in our behaviour that allow us to keep transmission rates low. This could include keeping some of the measures that have been put in place. Or introducing rigorous testing and isolation of patients to try to stay on top of any outbreaks. Developing drugs that can successfully treat a Covid-19 infection could aid the other strategies too. They could be used as soon as people show symptoms in a process called "transmission control" to stop them passing it onto others. Or to treat patients in hospital to make the disease less deadly and reduce pressures on intensive care. This would allow countries to cope with more cases before needing to reintroduce lockdowns. Increasing the number of intensive care beds would have a similar effect by increasing the capacity to cope with larger outbreaks.

Here is another report on the endgame, this time from the Guardian. Like the BBC, it also suggests that there are three possible endgames, but they are not quite the same; they don't mention the 'do nothing' option, but they do add an option 'trace and track'. That option can only be followed when the number of people infected is very mow and borders are closed. It's been tried by many countries but has failed to suppress the outbreak effectively. With regards to the 'mitigation' option, which the Guardian article calls 'flatten the curve', the article includes a reference to the Ward Plan. They forgot to mention my name, but the essence of the Ward Plan is there. Judge for yourself: "Isolate everyone over 60 (the age group most at risk), and infect as many younger people as possible, and then hope that the disease dies out." The idea that we should infect as many young people as possible is based on the idea that only a small fraction of young people would need hospitalisation or would die. But this article in French says that a study (published February 9) of 1099 hospitalised Chinese coronavirus patients showed that half the patients hospitalised were less than 50!! According to a joint study by the University of Oxford, Imperial College and Queen Mary College London, published last week, of 1000 people who died with the virus, 1 in 5 were less than 60. The same statisticians calculated the mortality rate for over 60s as 1.33% and for under 60s as 0.39%, meaning that the mortality over 60 is about 3.5 times greater than for under 60s. With hospitalisation and death rates like these, maybe the Ward Plan isn't such a good idea? The Guardian article agrees, saying "It’s not really plausible. There would be continued pockets of infection in many places, and they would quickly turn into localised outbreaks, particularly in nursing homes. It would be very hard to keep everyone over 60 separate from the people who provide them with food and services (who are likely to get infected) for months. And of course there will be some deaths among those under 60."

Looking on March 31 at the chart of daily new cases in the United Kingdom here one gets the impression that it might be leveling off at about 2500 new cases per day (???). Hopefully that's not above the saturation limit of hospitals. If only one in 20 cases is being detected, say, then that would be 50k new cases per day. If that were to stay steady, how long to achieve herd immunity, if that means 60% of the population infected?

66M *0.6 = 39.6M 39.6M / 50k = 792 days = 2.2 years. We really need that vaccine! (Note that I've ignored the maybe 0.5M existing cases in the above calculation since that is small compared to the 66M UK population).

UPDATES

Since this page was getting too long and since I'm sure that you check this page regularly and that you are also getting coronavirus information elsewhere, I've moved the updates to this page. Good daily updates can no doubt be found on many sites such as the Guardian.