Keeping one day ahead of the curve

As soon as the government released its modelling of the pandemic a few days ago, I realised something was badly wrong. The modelling showed infections increasing even under lockdowns, which obviously wasn’t happening. The crucial parameter here is R, the number of new infections generated by each existing infection. If R is greater than 1, the number of infections grows exponentially, but if R is less than one, it declines, eventually approaching zero. The knife-edge case is R=1, when the number stays constant.

On checking the paper on which the modelling was based, I found that it did indeed assume R>1, even with social distancing. This was less surprising when I realized it was based primarily on data from the initial outbreak in Wuhan, before the lockdown in China had taken full effect. (I later discovered that the report had been given to the government in February, which makes its release now rather pointless).

I quickly drafted an article explaining the importance of R and the fact that the modelling was out of date. I thought it would attract plenty of interest, but in fact it was very difficult to place. A lot of editors were unwilling to challenge the government on this. I eventually managed to get it run in Inside Story.

My time outside the tent didn’t last long. Today, the Deputy CMO Paul Kelly gave an analysis that matched mine almost exactly, and effectively abandoned the “flattening the curve” strategy in favour of eradication. The only difference is that he thinks R is “on the cusp of” falling below 1, while I think it’s already there. Some conservativism is called for here.

This has been the whole story of the pandemic for me. Almost every time I’ve criticised the government for not doing or saying something, they’ve got it right (or nearly right) a day or two later. Compared to my usual experience of waiting years for any kind of vindication of my argumetns on policy, it’s a strange feeling.

37 thoughts on “Keeping one day ahead of the curve

  1. >R is “on the cusp of” falling below 1, while I think it’s already there

    It doesn’t matter either way, because it’s been caused by the lockdown. Are we going to make people prisoners in their homes and until a vaccine is found? A vaccine might never be found. Eventually the lockdown will have to be lifted and we are going to have the manage the cases and accept that people will die. The question is how many deaths are acceptable. And even if miraculously we can achieve eradication within the country, are we really going to close our borders until a vaccine is found?

  2. J,Q., Correlation is not causation. Are they listening to you in particular or to the thousands of scientists, epidemiologists and doctors who must be telling them the same thing? As you prove, it does not even take a doctor or epidemiologist to pick the flaw in their model, just any kind of competent mathematician will do. Even Grade 11 maths would be more than enough. Any high school senior in science or maths could do it. If the people involved could not see such a fundamental flaw in their model it is very disturbing to say the least. Are they completely stupid? What are other conclusion can we arrive at?

    On the other hand, it is at least good that the erroneous model has suggested overkill not under-kill.

  3. “More than 6100 people in Australia have contracted coronavirus”

    I’m so sick of this statistic being reported. John, can you please criticise the government for not focusing on the far more relevant statistic – the number of people who have contracted COVID-19 in Australia, not the number of people in Australia with COVID-19. It would be great to start seeing the number that actually matters for decision making appearing more in the media (in a day or two).

  4. I would’ve thought that enough folk would catch the virus thru illicit interactions, supermarket visits, hospitals, emergency service workers, police, taxis, public transport, petrol stations, passing each other in the street etc. to make getting to zero infections impossible.

  5. I don’t see any great problem with a year or so with closed borders. We can get very good at quarantining those who do come in and at contact tracing for the few exceptions. Goods will still be able to come in and out, and possibly even long-term visitors like students.

    I hope the irrelevance of the modelling reflects the usual government fear of publishing any modelling and not the poor quality of what is actually informing their decision making. I find it odd that we haven’t heard more talk about targeting zero. I assumed it was because Scotty doesn’t want the embarrassment of aiming for something and missing, but maybe it’s because they haven’t figured out that it’s the best strategy.

  6. @Hugo I think it’s pretty hard to get it from any of those sources. If you think about colds, we mostly get them from colleagues, clients, friends and family. Maybe you occasionally get one from a stranger, but even then it’s much more likely that was on a plane or at a crowded bar than the supermarket. One thing we’ll realise this winter is that we basically choose to get the flu.

  7. Hugo,

    If the R0 can be got below 1.0 for long enough we invoke exponential decay which fortunately can be as rapid as exponential growth. An R0 of 0.5 shrinks the epidemic as rapidly as an R0 of 2.0 expands it. In roughly the same time (plus about a month) that 1 person gave rise to 1 million infections, 1 million can theoretically dwindle to one and then none. It’s not quite that simple of course. Reservoirs of infection can persist where R0 is over 1 unless they are dealt with. Prisons may be an example. Slums may be another example and so on. The maths modelling no doubt gets much more complex than I could handle but the basic principle holds , some epidemic diseases are eradicable or nearly so.

    Completely or partly eradicated human diseases globally include;

    (a) Smallpox;
    (b) Polio;
    (c) Guinea worm disease, dracunculiasis;
    (d) Yaws;
    (e) Malaria (in some regions and countries only).

    Examples of an eradicated respiratory disease of the infectiousness of COVID-19 might not exist I grant. But with effort we could reduce it to a very low level and keep it there. If that means remaining hermetically sealed from the world for two years then so be it. We produce enough food and we can restart many necessary manufactures. A reasonable level of national self-sufficiency and semi-autarky is all that is required.

  8. Ikon,

    To be clear, I think COVID 19 can be eliminated in Oz and possibly worldwide once we have a vaccine.

    ps. Just saw Prof Quiggin on SBS news. Great job, professor!

  9. The Chinese Dictatorship is lying through its teeth about this virus and the pandemic. Our criticism of China should be severe. The Western world should place severe long-term sanctions on China. Those who would argue against sanctioning China are appeasers of and apologists for Totalitarianism. There is no contradiction at all in Democratic Socialists being opponents of State Capitalist Totalitarianism in China (or anywhere else)..

  10. John, You have delivered a strong and accurate message. Well-done. Let’s hope that the recent trends toward low infections continue and that the small number that does occur can be rigorously pursued. Infections today are 1/5th the level they were only 12 days ago.

  11. I don’t see eradication as a attainable goal in a world as connected as ours. Not unless we are prepared to abandon the tourism and foreign education sectors, and curtail trade (and we no longer make – or even could make – a great many things on which we depend). Sure the air and sea cargo will not bring in the virus, but the technicians, advisors, sales-people, aircrew, seafarers and so on will – unless quarantined or they bring their vaccination certificates with them.

    The virus will find a home in pockets where tests and distancing are scarce – Indonesia, red states in the US, Africa, breaking out periodically as it transfers to visitors who travel on. We don’t even know if a vaccine is possible or, if it is, if it lasting.

    We can aim to push this round to near extinction, and then keep it low with stringent controls.

  12. JQ, on this occasion I believe you have not picked a problem or an error.

    IMHO, the problem lies with pressure having been put on the government to release ‘the model’ without asking how virologists and epidemiologists are using ‘the model’. That is, the appropriate question would have been to ask for an overview of the methodology.

    As could be anticipated (and it was anticipated by many of my friends, not all of them are academics), points such as that brought up by you would be talked. But they are irrelevant. As I noted in a comment in an earlier thread, the parameter R is a theoretical parameter in a general model that is based on prior pandemics. Even I could figure out that much. The parameter R is time dependent. Given that Sars Cov 2 is a new virus, the best available data to be plugged into the general model is the data before China took lockdown measures. To observe the effect of mitigation measures one has to run at least 2 ‘models’ with time dependent parameters.

    The above is oversimplified significantly. I understand in the meantime virologists and epidemiologists have collected data from sources other than China. They have learned more about the new virus and they continue to do so. ‘They’ is the appropriate term because, I understand, information is exchanged internationally among these scientists. In their advice to governments, they have to take into account the quality of the data regarding extent of testing, death rates and the quality of this data, and mitigation measures in their local environment, while taking note of what happened elsewhere, and at all times compare the short term predictions to hospital capacities, including protective clothing, masks, ventilators, etc. I assume with great confidence that this involves professional judgement and the word ‘complex task’ is appropriate here.

    I do hope the release of ‘the model’ isn’t going to end up in the same mess as that associated with climate models.

  13. and knock it off with blame the Chinese. Sure they made some mis-steps, but anyone who thinks that a new disease with a week or more’s asymptomatic transmission would not have escaped well before the alarm was raised – or that other governments would have sprung into immediate drastic action – is living in fantasyland.

  14. Peter Thomson,

    Knock off with the criticism of a totalitarian regime!? No, I will not. Do you think it’s okay that China is run by an oppressive totalitarian regime and that this regime is beyond criticism?

  15. Iko – not at all. Criticise their totalitarianism all you want. Just don’t blame them for this outbreak.

  16. Iko

    At least the CCP can get the virus to run on time.

    More seriously, epidemic skulduggery by governments is very common. Italy managed to entirely conceal the outbreak of a 1911 cholera epidemic in Naples for decades. In 1918 Chile decided the pandemic was typhus, not flu, that the imaginary typhus pandemic was all the fault of workers living in unhygienic conditions, and sent in armed sanitary brigades to demolish working-class suburbs.

  17. Doctors in Wuhan noticed the disease as something other than viral pneumonia in mid December. By late December the authorities had notified the WHO of a new disease – cause and transmission unknown. The genetic sequence identifying it as something other than SARS (which does not transmit asymptomatically) was done by 7 Jan. It was provided to other countries on 12 Jan. The first cases outside China occurred a few days later (Thailand 13 Jan, South Korea 15 Jan).
    Wuhan was put in lockdown on 23 Jan. Wuhan is a major industrial hub and Chinese New Year was in full swing.
    In essence, by the time they knew what they were dealing with, it had already escaped outside China.
    We put a ban on direct entry from China on Feb 1.

    I can’t think of any government which has moved as fast as the Chinese on this – we pursued incremental measures for at least another month – they went from uncertainty to discovery to full crisis mode in about three weeks.

  18. There can be little doubt that this covidvirus is a Chinese plot for which the Chinese should be highly praised not condemned. They are more than justified in unleashing this form of asymetrical warfare.
    One could try to deny that this attack has nothing to do with the blatant US act of war against the Chinese ally Iran and potential ally Iraq, They would say that this virus made the jump to humans months before the unjustified attack on General Soleimani. But if the Chinese intellegence agencies knew that the attack was in the works they would have released the virus for plausible deniabiltiy. China has finally tired of appeasing the USA and its allies.
    It has been reported that this miracle virus was not developed in a labratory. It was not neccessary for the Chinese to have developed it in a labratory. It was only neccessary that they study it. It would not be at all surprsing that the Chinese have already developed a vaccine for the virus which they will secretly sell to a German company at the appropriate time to hide the origin of the vaccine.
    We can also be quite sure that UK Prime Minister Boris Johnstin was not sickened by the Coronavirus.
    He might have very well had the coronavirus but he was actually sickened by a bacteria that was introduced to him by someone in his inner circle that has symptoms very similar to the Coronavirus. It might have been an assination attempt that was thwarted by the actions of the doctors treating him. Or it might have had some other nefarious purpose like creating sympethy for the the Prime Minister.
    What a fighter he is, is how the public perception could be managed.

  19. Further to Ikonoclast’s post at 8:22 PM and the content of the associated video clip, The Guardian published a piece a few hours ago, which contains some details as to what happened in mainland China and the source of the information.

    The first case of Covid-2019 in Europe was confirmed in France on 24 January. It concerns a person who returned from Wuhan on 12 January 2020.

    France introduced a surveillance method (reporting and contact tracing) by 10 January. Now France is one of the worst affected countries in Europe in terms of number of death per million people. In what sense was France slow to react?

    When Australia reacted by closing the border to travellers from mainland China, the Chinese Embassy complained with reference to the WHO.

    What prevented China to introduce an outward travel ban for all its citizens at the latest on 31 December 2019 for a period long enough to study what was going on?

    There is a lot more to be learned from this global disaster (and I don’t believe the findings will have anything to do with Curt Kastens’ theories).

  20. The origin of COVID-19 is zoonotic. It is not from a laboratory. This is known from the structure and functioning of the spikes on the virus (for gaining access to the host cell). Computer programs theoretically capable of virtual engineering such viruses were fed the COVID-19 structure and predicted low infectiousness. The operation of the host cell enzyme furin in activating the spikes was not predicted or predictable, given the current state of the models. Thus it seems highly unlikely to impossible that it was human engineered.

  21. Even with the best will and best possible actions, the Chinese Government might not have stopped the virus from spreading in China and to the world. However, without the best will and best possible actions, the Chinese Government made it certain the virus would spread globally, even if that was not their deliberate intent. A certain degree of culpability still inheres in that.

    Ernestine Gross refers to France and asks, “France introduced a surveillance method (reporting and contact tracing) by 10 January. Now France is one of the worst affected countries in Europe in terms of number of death per million people. In what sense was France slow to react?”

    Without knowing the fine detail of France’s subsequent actions after that first apparently timely action we cannot answer that question. However, I noted* during the start of Australia’s responses to COVID-19 that Australia was introducing measures much too slowly. Yet, here we are with Australia appearing to be one of the most successful responders to the virus. Clearly, further factors are at work. My own theories are that;

    (a) Australia has a low population density overall and major pop. centers are well spread out.
    (b) It still being summer here slowed the spread.
    (c) Our contact tracing and self-isolating have been good once started? Maybe.

    It also seems that some countries with very direct Wuhan connections were infected early and often and this played a role. I’ve heard of a report (I’ve not confirmed it) that the Lombardy region’s garment industry has garment-workers from Wuhan in Lombardy (so that the label can say “Made in Italy” while paying low rates).

    A lot of this points to a world that is too connected by capital and labor not to mention the veritable plagues of tourists who descend on cities from Rome to New York and everywhere else.

    * Note: My wife would scoff at the idea that I “note” things. “You rant,” is her judgement and we have an agreement that I leave the lounge room as soon as called out for it.

  22. Ernestine – odd diseases pop up all the time. Most are not very contagious and are – in functioning health systems – rapidly contained. EG SARS, H1N1, Ebola, Hendravirus all in the last decade or so. This one is more or less tailor made for global transmission – long asymptomatic period, highly infectious. It almost certainly escaped China in November, when it just looked like some form of viral pneumonia. That France reacted so fast and yet still got hit so badly confirms this.

    We collectively will, if sensible, build a lot more resilience into the system. Then – December 2019 – it would be a brave call to send a shock wave through the global economy every time a health problem of unknown aetiology appeared.

  23. Peter Thomson,

    The phrasing “odd diseases pop up all the time” glosses over the fact that most of these diseases are zoonotic. Zoonoses)are caused by pathogens which spread from animals to humans. Because we use and exploit animals, both domesticated and wild, often en masse and in industrial quantities and manners, the chances of these diseases arising are increasing all the time; especially as we continually encroach on wild habitat, meet new animals… and eat them.

    If it escaped China in November, then some of what you are saying follows logically. I am not sure we can say it escaped that early but I guess we also cannot say for certain it escaped later.

    “We collectively will, if sensible, build a lot more resilience into the system.” This is true and it must not only apply to lifting medical research, spedning and epidemic preparedness. It must extend to changing our food systems: both the industrial food system of capitalism and the bush-meat / wet market food systems of China, South East Asia and Africa. The Indian sub-continent seems less prone to these zoonotic outbreaks (though not to other kinds of outbreaks) due to the number of food taboos in Islam, Hinduism, Buddhism etc. and the number of Hindu, Buddhist, Jainist and other religions which feature high levels of vegetarianism. There is obviously an almost timeless cultural wisdom in some of their food taboos. We would do well to pay attention. So would the Chinese.

    A world convention to ban bush-meats is needed. Ways to get protein to the poor in those regions must be devised. Meat eating needs to decline and vegetarianism be encourages where feasible. Getting the right protein and fats to children expecially might mandate some continued meat eating.
    Getting bush-meat off the menu is a necessity. Banning wet markets should be on the to-do list too.

    The definition of bush-meat is tricky. Would crocodile and kangaroo count? I have eaten both though not very regularly. There is an argument that if we stopped grazing beef cattle and ate kangaroo we would be healthier and methane emissions would drop.

  24. Right and the no one in the Chinese Intellegence Services have ever Read the book, How to Win Friends and Influence People written by the Chinese Author Lao Sun over 4000 years ago. Or was the authors name Lie Sin? Could he have been a Catholic Missionary? Or, perhaps a Catholic mercinary?
    The release of the virus is such an obvious event of asymetrical warfare it is pathetic not to recognize it for what it is. I heard two Doctors on a podcast (a Peter Attia podcast) saying that it does not make any sense to say that this that a virus that only kills old people would be released as a deliberate act of war.
    It does not make any sense to them because they are doctors, not military strategists. They have obviously never read the book that I refered to above.
    There is no guarantee that the Chinese and their allies will win this war. The US leadership and thier allies are also extraoridinarily devious. A perfect example of that creative deviousness was to sabotage the Ukrainian Airliner that was shot by the Iranians in January. That was part 2 of the plot to overthrow the current Iranian Government. Setting up that operation with the current Ukrainian government was why Biden’s son has had such close connections with the Ukrainians. Ohh no Curt, how can you say that it was just a big coincidence that there was so much skullduggery going on between the US and Ukraine in 2018 and 2019. Those who can not attribute the absolute worst motives and the most incredibily diabolical actions to the US government leadership and its allies are not as the Buddhist say awake.
    The events of the past two months are the first time in decades if not in centuries that these “western” leaders have suffered a serious setback. There are a lot of talented people in China, Russia, India, Iran, Cuba, and Venezuela. But there are also a lot of talented people in the USA, UK, Israel, Saudi Arabia, France, Germany, Japan, Korea, Canada, and Australia as well. Which leaders will have the pleasure to still be in power when the biosphere collapses is now hard to say at this point.

  25. JQ, what you are discussing is very well understood by health departments, and has been from the beginning.The initial goal of physical distancing is mitigation, holding the infections down to delay the peak of the outbreak while you prepare the health system, and to reduce the peak below the breaking point of the system (when you go in with serious pneumonia and there are no ventilators left, your probability of death massively increases). If the outbreak has not taken hold, you can change the goal to suppression (which is what everyone is hoping for), with a goal of elimination locally, and controlling all entry (e.g., mandatory quarantine).

    Has the outbreak taken hold? We don’t know yet. It depends on the extent of community transmission, and we don’t know that because you don’t know who to test (unlike people coming from overseas, or who front up with pneumonia). The best you can do in Australia (for now) is to track the number of people who test positive without a known contact and to start testing people with lesser symptoms in hot spots (already commenced). NSW Health has a moderate number of unknown source test positives but is increasing the resources to follow these up, potentially biasing the data series (i.e., when there were fewer resources more get erroneously identified as without contact, so as you add resources it may look like the infections are going down when the opposite is true). This is why we are on hold for a few more weeks.

  26. By the way. Almost everyone assumes that the Chinese are lying about this virus has impacted thier country. But if the Chinese population had been secretly by and large vaccinated against it the Chinese would have no need to lie about the minimal impact on China.
    Even the name Covid-19 smells. Covert Intellegence Device 19. I bet that if we had a high enough Chinese Security Clearance we would find out that SARS is an acronym for something other than what it stands for to the public.

  27. I am certain that Qld health is now testing more widely ie everyone with a fever. this should give some idea of community spread. so if people going in with the flu or an infected toe are being screened we should get an idea of the real extent of the virus.

    The concept of “herd immunity” while deeply flawed would have its place IF (and it is a very big if) we could be sure that 80% of the population have had the disease.

    Perhaps also we may be lucky and find a way to predict which people will get the disease severely.

    Joking but? perhaps we have a new role for those unuseable cruise ships. Corona cruises where you put say lots of 14 year olds on a boat for two months, staffed by recovered crew members (there seem to be PLENTY). So they get the virus without any risk of infecting granny or Uncle Fred.

  28. What i´m hearing in Germany, where admitly the virus admitly is more widespread so that it might well be more reasonable to give up hope on suppression is a very ugly beating arround the bush debate. One politician said in exact that same order one would also have to consider the financial economic and psychological effects of containment measures (implying one better does away with them right now). The sad part about it – no measures with serious impact on the economy were taken. Private live is closed down completly, no ones allowed to meat anyone besides his household, so is mental health support and the like, but there is no ban whatsoever for any work related activities, no mandatory home office, just a suggestion and public transport is still crowded on lines used by the lower social class to go to work. The car industry did shut down mainly due to a demand shock, not for to health concerns. One of the major news shows tells us all the time that its inevitable that millions will get the virus and that all efforts can thus just aim at flatteining the curve. One virologist did a press conference recently with half baked results of a new study presented in a way tailored to suggest one should just go with herd immunity. As someone without a job and you might have guessed it some mental health issues for which i´m used to seak some regular support(nothing too bad no worries), i´m mighty pissed that i´m sitting at home for some 3 or 4 weaks now, which would have been enough time to go close to zero if we had dared to touch the almighty private economy. That includes the basic supply sectors. Shopping and paying looks likes an area of risk to me. A) Many use public transport to get there, B) people aint particular careful C)people go shopping all the time because its the legal way to meat people…… So i don´t understand why there wasn´t a t least some one time a weak on shop one one person per household rule, or an outright mandatory home delivery system run by the government. Oh yes, also theres the issue of no one dare to impose anything on the elderly poltical issue. Of course they all still go shopping, no matter how many offer formal or informal to do the shopping for them. No chance there without an outright ban for say anyone above 60 combined with goverment run home delivery. I´m speaking in the past, because lets not kid ourself, we´re getting closer and closer to the point where it´s hopeless anyway to get anything but “flattening the curve”.

  29. In Australia it is clear the politicians don’t understand what is going on but there are experts working hard behind the scenes to help keep us safe.

    In the US the leadership doesn’t understand what is going on and had ignored expertise and frequently undermined it. This is why their death toll, per capita, is going to be over 200 times ours.

  30. Epidemiologist demolishes the idea of herd immunity without a vaccine. Well, it could possibly occur but at COVID-19 death rates it would be and is disastrous (as we are now seeing).

    That leaves only;

    (1) Isolation and distancing.
    (2) A vaccine.
    (3) Eradication.

    Next (not in his article), three more terrible possibilities exist.

    (A) A vaccine might prove impossible. There is no certainty it is biologically or technically possible. No coronavirus has ever yet had a vaccine made for it. Of course much greater effort will be input now.

    (B) Adult immunity might wear off and relatively quickly too, meaning you could get infected over and over as with coronavirus colds (and mutating flus) for example.

    (C) The disease might be seriously bi-phasic which means the second time you get it is often worse, like dengue hemorrhagic fever for example.

    Take (A), (B) and (C) singly or in any combination and this is a doomsday virus scenario for global civilization unless the disease is ruthlessly eradicated. Hence, eradication has to remain on the table as the ONLY KNOWN SOLUTION right now. We have to eradicate totally on the assumption that (A), (B) or (C) in any combination might be the case. Be prepared for isolation for 1 years, 2 years or indefinitely.

    Australia might have to isolate from the world for a year up to a generation. Nobody knows yet.

  31. Awaken and disCOVer the true meaning of being born again.

    That was channneled from Robert Levison for a little levity.

  32. “The knife-edge case is R=1, when the number stays constant”.

    Ah… not quite. Consider the Galton-Watson process (I have to resist writing Galton-Simpson). With that, as repeated composition of probability generating functions tells us via the recurrence relations they give for expectation and variance, you get the following cases:-

    – the expectation grows exponentially and the variance grows exponentially, but twice as fast;

    – the expectation shrinks exponentially and the variance grows shrinks exponentially, just as fast;

    – the expectation is constant (just as you say), BUT the variance grows linearly – that knife edge case.

    But there is a simple graphical demonstration that the population will eventually go to zero in that knife edge case, so “constant” is misleading.

Leave a Reply

Fill in your details below or click an icon to log in: Logo

You are commenting using your account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s