The awful arithmetic of herd immunity

The ABC has an article quoting University of Melbourne epidemiologist Tony Blakely as saying (approvingly) that the object of the current “flattening the curve strategy is to smooth the path to herd immunity. Key quotes

You don’t go in too hard because you actually want the infection rate to pick up a bit and then hold,” he said.

“What they’re not saying is [that] ‘flatten the curve’ likely means [that] by the time this is over, 60 per cent of us will have been infected, to develop herd immunity,” he said.

The arithmetic here is pretty horrifying. 60 per cent of the population is 15 million so with a 1 per cent fatality rate, that would be 150 000 deaths. The number surviving but with long-term lung damage could easily be over 1 million.

It gets even worse. If herd immunity is supposed to be achieved over 12 months (by which time we are hoping for a vaccine) that would imply 40 000 new cases every single day. If even 10 per cent required hospitalization for several weeks, they would fill every bed in the country.

As for intensive care, we have a total of just over 2000 beds. Even with a hospitalization rate of 1 per cent, they’d be full in five days. And given that 1 per cent is the estimated fatality rate with treatment, that implies triage on a massive scale, which in turn would greatly increase the death rate.

This is simple arithmetic. If Blakely’s explanation of the government’s strategy is correct, it should be spelt out.

58 thoughts on “The awful arithmetic of herd immunity

  1. The other country (apart from Taiwan) that has done well – at least in terms of deaths from CV – is Germany. Many infections but relatively low death rates. Like Taiwan, Germany has been obsessive in tracking down the contacts of anyone infected. Also, Germany has isolated seniors early on. Seniors are 7% of the German population but only 3% of deaths – this avoids the horrible situation in Italy. Morrison has tried the same sort of move this evening – people 70+ (or those with chronic health problems, those 60+) are asked not to leave their homes at all apart from medical trips. A good idea particularly if others (safely) help them with their shopping and other tasks.

    Germany has lots of hospital beds too but, if total infection rates rise, the future may be less pleasant than it is now. But so far it has done relatively well.

  2. The only comments I have seen by anyone in authority about the long term game plan are from the ACT CMO, who said the plan is to let the virus run for six to nine months to develop herd immunity. On ventilators and intensive care, the Deputy Commonwealth CMO said on the last QandA that hospitals can easily double number of intensive care beds, and probably triple them.

  3. Seen – the herd.

    The first thing to be nationalised – our data. Or risk the chilling effect of recalcitrants hiding. And fbook owning it!

    “Governments could track COVID-19 lockdowns through social media posts

    “A research group scrapes more than 500,000 Instagram profiles in Italy to see if people are abiding by the quarantine.

    “It provided those images and videos to LogoGrab, an image recognition company that can automatically identify people and places. The company found at least 33,120 people violated Italy’s quarantine orders. 

    “The research project scraped data from 552,000 Instagram profiles in Italy and gathered 504,592 Stories posted to these accounts between the dates of March 11 and March 18. Italian Prime Minister Giuseppe Conte issued thenational quarantine on March 9. 

    “The researchers said permission to collect the data wasn’t necessary because the posts are public. Users weren’t asked to give their consent.

    “Facebook, which owns Instagram, is looking into the practice.

  4. I suspect it will take longer than six months to develop herd immunity IF we bend the curve andkeep the cases under the medical system’s ability to cope with the peak.

    “Typically we’re shooting for 80 to 90 percent of people who are immune before you get to the level where you’re going to control that contagious disease from happening,” Karen Hoffmann, immediate past president of the Association for Professionals in Infection Control and Epidemiology (APIC).

    Let us assume the lower bound of 80% of Australia’s population which is 25,600,000 (rounded number. 80% is 20.500,000 (rounded up a little). So we need 20,500,000 infected to get herd immunity on these assumptions. 5% of cases will likely be serious or critical. Let us call that 1,025,000 people for round numbers. We can assume all these will need ICU beds or at least hospital beds. Let us assume that 20% of these cases need ICU beds and 80% need other hospital beds. Let us further assume that we can more than double ICU beds to 5,000 and have 20,000 other beds for “merely” serious cases. That’s 25,000 beds. All these beds are in addition to beds we will continue to need to treat cancer, heart attacks, strokes, car accident victims, other dieseases and critical/urgent surgery cases.

    Let us further assume that we can accurately “toggle” or “throttle” the cases arising to keep the number serious and critical at precisely the capacity (a simplifying assumption). Let us assume each bed stay is one week on average (another simplifying assumption and maybe optimistic or pessimistic).

    Thus the number of weeks to develop herd immunity and stay under the hospital bed limit is 1,025,000 divided by 25,000 equals 41 weeks. Let us assume plus or minus 10 weeks. It could take anywhere from 30 weeks to 50 weeks. Since we probably need more than 80% herd immunity in reality and other black swans to this situation might well appear, I would settle for 52 weeks, a round year. This medical crisis probably runs for a year at critical level. Then there’s the economic damage during and after. it’s likely to be 18 months until a vaccine if it can be created at all.

    I’m planning for a year in isolation and taking great care even after that. I’m 65 (nearly 66) with no serious pre-existing conditions except for benign prostate enlargement and an umbilical hernia, both of which can kill a person if they flare up and no emergency surgery is available. Tough bickies as they say. We took a big bite out of the biosphere. Now it’s taking a big bite out of us.

  5. Good news Ikonoclast. You won’t have to go into isolation for a year. On the basis of the data of the last 7 days we have bent the curve dramatically and we should be able to reduce the growth in cases to zero by the end of April if we keep our pedal to the floor. From March 13 to March 24 the number of cases of covid 19 was increasing at a pretty consistent 24% per day. Since March 24 the growth per day in cases has been dropping pretty consistently and is now (30th March) at 7% per day. ie we’ve gone from a doubling time of 3 days to a doubling time of 10 days. They say quite rightly that one swallow doesn’t make a summer, but we now have a consistent trend over a 7 day period, so I think we have grounds for being positive. If we keep controlling border entry and we aggressively pursue the contacts of the few hundred apparent community transmissions, we should be able to bring the growth rate in cases down to 0% per day in a few weeks time.
    I could be wrong, and there may be a large reservoir of unknown cases of covid 19 infection which could explode on us, but given that the incubation period is 4 to 8 days, if there was a large reservoir of unknown cases we would be expecting to see some signs of it in the current numbers. And we’re not.
    Every day we have a reduced growth rate gives us more confidence there is not a large reservoir of unknown cases, so we should know in a week’s time whether it is, or is not a problem.

  6. Daily new cases suggest no sustained bending of the curve. The data is noisy and the daily numbers are bouncing around but the trend still looks bad. Look at daily new cases and active cases here for Australia.

    The next four weeks will truly tell the tale. I will be astonished if we do any better than Germany on a per capita basis. I’m prepared for very bad news. That’s what I think is coming.

  7. Unfortunately the Iko index, deaths/(recoveries + deaths) can’t be calculated properly. As I write NSW has four recoveries and Victoria has 422. Obviously recovery is defined or recorded differently in each state.

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