Coronavirus

As Lockdowns Are Lifted, Is the COVID-19 Reproductive Number Rising or Falling?

Two models generate strikingly different estimates.

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If you are a critic of COVID-19 lockdowns, here are some numbers you will like. I also have some numbers you will not like as much, which I will get to in a minute.

According to a model by researchers at the University of Utah, the "real-time reproductive number" for the COVID-19 virus—the number of people infected by the average carrier—has fallen in Florida since the state began loosening its restrictions on businesses and individuals, from 0.98 on April 30 to 0.5 on May 26.

When the reproductive number falls below one, that indicates an epidemic is waning. The daily number of new cases can be expected to decline, and eventually so will the total number of active cases as previously infected people recover.

In Texas and Georgia, two other states with big populations that lifted their lockdowns on April 30, the pattern in the University of Utah model is initially similar but less encouraging in the last few days. In Texas, the model shows the real-time reproductive number falling from 1.13 on April 30 to 0.79 on May 22 and 23 before climbing to 1.32 on May 26. In Georgia, the number drops from 0.96 on April 30 to 0.78 on May 24, then rises to 1.01 as of May 26.

If you are a lockdown supporter, here are some numbers you will like better. According to a different model, this one produced by the independent data scientist Youyang Gu, the reproductive number in Florida rose from 0.96 on April 30 to 1.07 on May 26. Gu's model also shows the number rising in Texas (from 1.01 to 1.07) and Georgia (from 1.03 to 1.07) during that period.

Feel free to pick the numbers that reinforce your preexisting beliefs. If you want to support the view that lockdowns are overrated as a way to reduce transmission of the COVID-19 virus, the University of Utah model is for you. If you want to support the view that lifting lockdowns is reckless, Gu is your man.

Who is right? I don't know, but so far the Gu model has been remarkably accurate in predicting COVID-19 deaths, and the reproductive number figures into those projections.

The University of Utah model uses "a collated time series of daily state-wise positive
case counts from the COVID Tracking Project." The researchers calculate the reproductive number "using two complementary methods": the Wallinga and Teunis method, "which is forward-looking," and the Cori method, "which is backward-looking." The Gu model "builds machine learning techniques on top of a classic infectious disease model" known as SEIR, which starts by dividing the population into four groups: susceptible, exposed, infectious, and recovered.

As my colleague Ron Bailey has noted, the Gu model's projections "are considerably less optimistic" than the projections from other widely cited models. Historically, Gu notes, his model's COVID-19 death projections have matched the actual fatalities counted by the Johns Hopkins Coronavirus Resource Center much better than the model used by the University of Washington's Institute for Health Metrics and Evaluation (IHME). On May 2, for instance, the Gu model predicted 101,950 deaths in the United States by today, compared to the IHME projection (since revised) of 71,918. The current Johns Hopkins tally is 100,415.

The Gu model predicted that the death toll would reach 100,000 by May 25, and that happened just a couple of days later. It is now projecting more than 200,000 deaths by August 28. A projection by the U.S. Centers for Disease Control and Prevention, leaked to the press early this month, predicted that mark would be reached by June 1, which thankfully has proven to be excessively pessimistic. But if history is any guide, the IHME projections err in the opposite direction. They currently go only as far as August 4, when the predicted death toll is about 132,000, compared to more than 173,000 in the Gu model.

Since the Gu model's death projections incorporate its estimate of the reproductive number, it seems to have a pretty good handle on the latter, which suggests it is closer to the mark than the University of Utah model. Nationally, the Gu model shows the reproductive number falling from 2.26 on February 5 to a low of 0.91 on April 11, then beginning to rise on April 28 and reaching 1.02 today. The University of Utah model puts the national average at 2.66 on March 20, falling more or less steadily to 0.8 on May 24 and 25 before rising slightly to 0.85 as of May 26.

While I would prefer to believe the more optimistic scenario, the Gu model's historical performance makes a compelling case for (relative) pessimism. Furthermore, it is plausible that lockdowns had some impact on virus transmission and that lifting them would boost the reproductive number. Whether that means they were worth their enormous economic cost is another question, especially since many of the COVID-19 deaths they ostensibly prevented may simply have been delayed.

NEXT: How This Bill Gates Coronavirus Conspiracy Theory Made Its Way from a Reddit Thread to Laura Ingraham

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94 responses to “As Lockdowns Are Lifted, Is the COVID-19 Reproductive Number Rising or Falling?

  1. Whether that means they were worth their enormous economic cost is another question, especially since many of the deaths they ostensibly prevented may simply have been delayed.

    You monster.

    1. “many of the deaths they ostensibly prevented may simply have been delayed.”
      Hate to break it to you, but death is unavoidable.

      1. Maybe with that attitude.

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      2. Don’t tell the Millennials. Or Greta.

    2. If we must eliminate all deaths from going to work it would require lowering the speed limit to 5 mph and only working where it is absolutely safe. When flu season arrives each year businesses would have to close and people stay at home. Are you willing?
      Flattening the curve was never about saving lives. It was about lengthening the time of infections over a longer period of time. At this point you get to decide if you want to die in poverty on the streets or take a chance of surviving the virus. You have a better chance of surviving the virus then you do poverty. Which do you prefer?

      1. At this point you get to decide if you want to die in poverty on the streets or take a chance of surviving the virus.

        Well, in a lot of states the choice is actually still between suffering poverty or suffering police interaction.

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    3. At the risk of sounding compassionless, from what I can find via google, nursing home patients seems to be a bit over a year without the impact of Covid. The odds are that at least half the current patients in Nursing Homes won’t live to see a working vaccine for this virus developed even if they can be protected from exposure to that virus perfectly.

      With 40%+ of total deaths being in nursing homes, which is probably undercounting since New York (where the state gov’t initally prohibited such facilities from really protecting their residents from exposure) doesn’t count NH patients who die after being transferred to a hospital, it’s hard not to say that a large number of those deaths were merely accelerated by a matter of months a bit by the virus.

      That’s not even getting into the fact that there was no version of “flattening the curve” that was ever designed to entirely prevent a significant number of people from ever getting infected. The fact of the underlying science is that we’re almost certainly going to reach “natural” herd immunity (widespread immunity due to most people having been exposed/infected and developing natural antibodies) before a working vaccine can be developed and mass produced in enough quantity to inoculate hundreds of millions (in the U.S.) or billions (worldwide) of people. Unless there are people dying from lack of access to care due to overwhelmed hospitals, then no amount of additional flattening would have saved any lives.

      Compounding with that are models and studies predicting that tens of thousands of people may well end up dying much sooner due to lack of available care caused by either the lockdown itself (since so many hospitals are prohibited from doing “elective” treatments like chemotherapy and organ transplants), or because media reporting has scared them to the point of not seeking care for otherwise treatable conditions (apparently the rate of people going to ERs with heart attacks is down about 40% since March, it seems unlikely that it’s entirely due to a much lower rate of people having heart attacks). Even the five kids who were reported to have died from “cytokyne storms” after having Covid-19 could have been saved if their parents hadn’t been too frightened to take them to a hospital for that treatable condition. Then there’s the likely uptick in drug ODs because 12-step meetings were shut down for months and addicts were forced into isolation (which most treatment professionals I’ve head talk on the subject say is a dangerous situation for people with such conditions), and the likely increase in suicides (calls to hotlines are up something like 500% during the lock-downs).

      Keep pretending that there’s no human cost to the lock-downs and feeling superior to anyone who doesn’t share your dogma, though.

      1. Thanks for reminding us of what we made clear back in March. Good to see the general population catching up.

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  2. Too late. No way we would have made the decisions we made in March with the models we have now. Models have already done their damage. Fuck them.

    1. Similar computer models are also be used to predict global warming and climate change consequences over the next 50 to hundred years. Isn’t that comforting? Somehow predicting the future always seems to be more of a guess then solid science. They also use computer models with much better statistical input for daily weather forecasts. The inaccuracy is why they use percentage rather then saying it is going to rain today. Predicting next week or next month is futile and if you watch the weather forecasts for just a few days in advance it changes everyday. However climate change is rock solid for 50 years in advance. I wonder if computer models have been compared in accuracy to flipping a coin?

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    2. Models of highly complex systems can be made to show almost anything depending on the assumptions used to make the subject matter simple enough to “simulate”.

      What really does damage is “leaders” who don’t really know any more than anyone else needing to project competency and appear to be “doing something”. Not that indecisive leadership tends to produce good outcomes when the masses are intent on following…

  3. No model shows hospitals getting overwhelmed. The lockdowns were about flattening the curve so hospitals don’t get overwhelmed, right?

    1. That was then, this is now.

      1. Bait and switch complete?

        1. There can always be another switch.

          1. See Minneapolis.

            1. Minneapolis looks like our covid response, lots of destructive action without all the facts. The medical examiner said the knee on the neck “contributed” to his death but I haven’t seen where he’s released the actual cause of death. I suspect the guy had a heart attack caused by his own 4 minute fight with cops while resisting arrest and the cops are being blamed for it because ideologues find that useful and criminals can justify their arson, looting and vandalism, kind of like the government is doing with their destruction of the economy and using the pandemic panic to slip in laws regarding airline emissions in emergency appropriations bills.

              1. suck a tailpipe pig fucker

    2. Now that they’ve sold too many people on the idea that secondary outbreaks would only happen if the re-opening were done “too soon”, and the experts have almost all weighed in with the conclusion that secondary outbreaks will follow re-opening whenever it happens, the authoritarians are stuck with no way to save either lives or face and a great opportunity to get more people accustomed to dependence on the welfare state (and thereby more controllable due to learned helplessness).

  4. What if we don’t care which model is right and just want to get back to our lives?

    1. /thread

    2. Who says any of the models are right? At this point I’m inclined to believe none of them and go with instinct. More people are going to end up dying from the economic impact of this over the next 5 years than will die from the virus before (if?) there’s a vaccine.
      There’s a new technocracy spreading that insists we listen to them and they should have powers that are contrary to our constitution without ever having proved that their models can accurately predict anything. It’s not hard science until it’s repeatable. So far the only repetition is failure to be accurate. I’m not saying we can never get there. Who knows? We’ve made incredible progress in the last couple of hundred years and the sky may be the limit. I am saying that right now, we’re not even close and the unbelievable hubris needs to be reigned in.

      1. Honestly, violence is the only answer.
        At least some technocrats need to be killed, because if they don’t fear retribution they’ll never stop pushing

    3. “What if we don’t care which model is right and just want to get back to our lives?”

      So much this. I am so sick of Sullum’s takes, because every. single. one assumes that there is some sort of discernable threshold at which point we throw libertarian ideals out the window.

      Sullum, read very carefully: Whether a virus has an R-naught of .75 or 2.0, lockdowns are an abomination of civil liberties. This number is a theory. It is a dream. It is a construct that CANNOT BE MEASURED, only inferred. It is a complete betrayal of libertarian values that you are looking for some number to justify whether or not we continue this lockdown.

      For God’s sake! People are being imprisoned in their homes. They are being denied the right to worship. They are being denied the right to assemble. They are being denied their god given right to earn a living. And you are comparing R-naught models?

      Why don’t you do your next article on the number of angels we could fit on the head of a pin?

      1. To be fair, you don’t need an audience to worship – the church is within you – isn’t that what the legend said?

        So everyone chomping at the bit to show the world how righteous they are can go ahead and get fucked in their own homes for all I care.

        It’s what Jesus wants.

        1. Tons of hate there, fella. You must really be getting off on all the death and destruction.

      2. +1000

        1. That was for Overt

    4. Do what they did in Michigan and be an American. The most devastating impact of the coronavirus will be the Democrats politicizing it. Instead of uniting and supporting one plan they have caused more fear and uncertainty. When shutting down the economy the effects were discussed and the devastating consequence compared to the gain. It was decided two weeks to a month would be damaging but save enough lives to be worth it to flatten the curve and allow hospitals to maintain. It was not to reduce the number of infections but to reduce the deaths if hospitals become overwhelmed with too many cases in too short a period of time. It is past time to start reopening. The fear mongering and division of the Democrats is simply politically motivated during an election year and not based on what is best for the country or people. If President Trump advocated for keeping the country closed down the Democrats would be screaming for reopening.

      1. Nah – all non-partisans see their antics clear as day.

        Not like we haven’t been witnessing the debauchery for the last four years.

  5. I do not find Gu’s numbers any more frightening than U of Utah’s. And I do not believe, as a Georgia resident, that we ever told that there would not be a slight uptick when we lifted our lock down. We expected an uptick in cases. There is not an activity that humans partake that does not come with risk of death. I am happy my state is opening and I am encouraged by both sets of numbers.

    1. The worse part is many of the “2nd wave is happening” hysteria is ignoring that testing has greatly increased. The percent of positive tests is steady or decreasing.

      1. It’s no longer about numbers or lives anymore – politics has transcended the entire paradigm.

        Besides, no one really cares about anyone’s life except their own. The majority has spoken – we ain’t at risk.

  6. The public’s tolerance for the shut downs may have fallen so low that an increase in the rate of infection due to the shut downs being lifted doesn’t really matter anymore.

    Yesterday, I linked to the story about how the Catholic and Lutheran churches of Minnesota sent a joint letter to the governor of Minnesota announcing their intention to reopen their churches in spite of the law. When you’ve lost the Catholic and Lutheran clergy of Minnesota, who else is left to support your lock downs? We’re not talking about the militia movement here!

    The chattering classes, the government bureaucrats, and the people who will support anything so long as they think the right is against it will stay behind you, but that is a very small slice of the American people.

    Everywhere in the world, people started isolating themselves before the government shut things down, and people will come out of isolation when they’re ready everywhere in the world–whether the chattering class, the government bureaucrats, or the progressives like it or not.

    1. I hope you are right. And I hope that people figure out that wearing a piece of dirty cloth over your face doesn’t do much to protect anyone and isn’t very healthy for the wearer either.

      1. Our state had a lock down and I went out to the store once or twice a week because masks were rare. Now things are “open” but masks are required, and I hate them, so I’ve voluntarily been home more since the lock down.

      2. No kidding. Wherever I go, I’m the ONLY person in that particular venue who is not wearing a mask. I feel like I’m surrounded by zombies.

        I refuse to wear one, not even as a show of “respect.” I just . . . can’t. So far, I’ve gotten away with it in Walmart, my local grocery store, the post office, and the computer shop. No one has been shitty to me. But my dentist, doctor, hairstylist, etc. are all requiring them. I just hope the mask idiocy ends soon so I can at least have my yearly physical, which is coming up.

      3. Aside from its political implications, I sorta like the anonymity a masks provided. I hope it stays this way forever.

  7. Florida got it right.

    That has to make NY and the hiders feel really dumb, being outsmarted by Florida.

    1. That is why the left hate Florida and Governor DeSantis and run propaganda and lies about him daily. He treated the state like people are not morons and let them make good rational decisions based on the circumstances of their local situations. Florida would have done really well if New Yorkers were not fleeing the failure in New York and attempting to pour into Florida. It has been amazing how well the left’s ally the fake news has given Cuomo and de Blasio a pass and even hero worship for killing off more Americans with stupid decisions then anywhere else. While Gov. DeSantis was protecting the vulnerable elderly Cuomo was putting infected people in nursing homes.
      The only thing Florida did was act rational and make intelligent decisions. South Florida was the hot spot because of New Yorkers and Europeans invading. There was also the unexpected arrival of spring breakers that were just let out early to keep from spreading it in their schools paying no attention and putting partying ahead of their health and life. What are colleges doing to our young people? Would you want someone that made that decision working for you?

  8. Both the 1957 and 1968 pandemics are estimated to have killed over 1 million worldwide each. And possibly much higher but uncertain.

    For a much smaller world population than today. This is the same except a different virus. No lockdowns before and life went on. If you still believe in a lockdown you are nothing but a government slave.

    1. But, we have all those cool commercials showing how fun and brave lockdowns are.

      1. Duck and cover!

        1. Shelter in place!

    2. My mother talked about the 68 pandemic and how they all worked and those who were sick went home including her until the boss called because he didn’t know where his ass was

  9. Whoever is right, the lockdowns are reckless and destructive.

    It’s as if people have forgotten that there are other things that matter in the world besides the number of people who die from one particular virus. Basing what you think about lockdowns solely on what is likely to happen with the virus is criminally stupid. You have to consider the whole of the effect of lockdowns on society in the short and long term. Just stop it with this idiotically narrow focus on the pandemic. It’s not the only thing happening or the only thing that matters.

    1. criminally stupid

      If only that were a legal concept!

    2. All of that Zeb. You are exactly right. The other thing that amazes me is that anyone is unwilling to just accept even a great risk if the alternative is living their lives like this. You are right, there is more to life than one disease. If avoiding that virus means giving up your whole life, you are better off dead.

      1. Amen brother.

      2. If we are going to use R-Naught to determine whether or not we get out of lockdown, how about we do that with Immigration? Once immigrant crime gets above…oh, 1.1x the number of normal crimes, we should probably throw free movement off the libertarian train. What about gun deaths? What is the number of school shootings before we just decide the 2nd Amendment doesn’t matter any more?

        1. (Sorry I wasn’t disagreeing with you John, I was trying to add on to your point that sometimes the intangibles will always tip the scales against hard math)

        2. Sure. I would love to see the stroke reason would have over that suggestion. They suddenly wouldn’t love science and numbers so much.

    3. “It’s not the only thing happening or the only thing that matters.”

      I tell my grade school aged children this and they get it.

      1. If that’s the case we need to begin indoctrination at an earlier age. Ideally, there should be no independent thought at any point in one’s life.

  10. models that don’t emulate what is happening in the real world should be thrown out and since all teh states that have reopened have reduce the rates why are we even looking at the models that say otherwise. I had this argument in real life once. my plans said the wall would be 2′ tall his forms were up and showed it to be 2′ yet his transit was saying 8′. i explained to him that the trainsit height had nothing to do with anything, many forget that fact and his form boards confirmed my numbers. why he didn’t look at his real world vs his math world I’ll never understand. which is why look at models the conflict with teh real world this is insane

    1. anyone remember the 3000 deaths a day that was to happen after opening up?? what happened to that BS

      1. a buddy yelled 3000 deaths a day!!! at me when I asked a group thread if anyone wanted to golf.

      2. Covid is the number one killer now and forever because for a week the numbers were high.

  11. Interesting that the Gu model rises to 1.07 for all three states…

  12. At least here in Wisconsin, increasing numbers of infections coincided with both the opening and increased testing. They tested the front line workers, then the essential workers, then those that thought they had symptoms then anyone that chose to show up, and all for free. So how do you decide the opening increased the numbers when testing was increased by that many new people? My guess is the percentage of infections remained the same, but the number of “reported” cases went up. Seeing all this testing was orchestrated to coincide with the opening and the rate of deaths is still not only low, but declining, there is no way to make a statistical statement that is worth a pinch of (add your own word here)!

    1. THat cannot be repeated enough. More tests means more confirmed cases. If you increase rates of testing, you should expect to see an increase in known cases. If it isn’t sufficiently randomized to apply to the population as a whole, testing results really tell us very little.

  13. Feel free to pick the numbers that reinforce your preexisting beliefs.

    OK, Sullum, I take back the last bad thing I said about you. That is some keen observational humor.

    1. He recycled it from a reader’s criticism of his work.

  14. it’s over. stop modeling and go outside.

  15. Is the Covid-19 reproductive number rising or falling?

    I’m going to go out on a limb here and say…. Yes.

  16. Feel free to pick the numbers that reinforce your preexisting beliefs.

    Like, say, 666?

    1. four. twenty.

    2. Actually I give 666 for my zip code when ever a store clerk asks for my zip code, which I find a very intrusive question.

      1. “What’s yours?”

      2. “Are you hitting on me”?

  17. Even if the Gu model is correct, 1.02 is not really that alarming a number. Additionally, what is the SEM of the Gu model and the University of Utah models, if they overlap, we can arguably conclude that there is no discernible difference. What both models do seem to be showing is that there is little evidence of a second wave at this juncture in time. Both show small increases but still minor during a 1 month period as people became more active.

    1. Not that alarming? You’ll never wash the blood from your hands. Never.

  18. With all the data now available computer models are still struggling to accurately give a prediction of future spread and deaths. Computer modeling software can be very accurate which means they are very sensative to input to calculate output. Some of the relied on models can not give the same output for the same exact input which is a terrible flaw and should have been thrown out.
    Knowing how sensative to input computer models are and accuracy requiring extremely accurate input how are scientist predicting climate change? The farther out models are required to predict the more sensative to input they become. Any slight variation in input can make a huge difference in output which grows over time.
    With the struggle to get good predictions of Covid 19 and all the different computer models giving different output with the same input some are bound to hit some data accurately just as flipping a coin will be accurate 50% of the time. Does this revelation of how computer models operate give you a good feeling about the predictions of the future of climate change or give you a little hesitation taking what they say as facts?

  19. How about we just ignore models and let people live their lives how they want?

  20. Who cares what the models project as long as they are using ‘covid death’ numbers that vary all over the place? Is it people who died ‘with’ or ‘from’ C19? Does someone killed in a traffic accident on the way home from a positive test count, or not?
    Politicians have incentives to both over and under report.
    Garbage in, garbage out.
    What counts is that silly old parchment.

  21. What if we don’t care which model is right and just want to get back to our lives?

    1. “Just do it.”

  22. I’m not impressed with either of these two models.What DOES impress me seriously is that, in comparison to the 200,000,000 deaths so direly predicted at the beginning of this charade, either one is solid proof the “experts” have no clue of reality, and were (and most coninue) simply throwing darts backwards over their shoulders, then taking those scores and launching the “lockdown” torpedo.
    When I read the early reports coming out of Wuhan CIty, the nonsense about the “wet market”, other factors in play over there, and the scary threatening words being printed… I was pretty sure we were in for it, and that government and big medicine were going to lock arms and torment us… early predictions were for two thousand times what we’ve seen so far. The numbers are not going upward like a Saturn rocket as predicted, the pool of highly susceptible victims is quite small and narroly defined.

    One thing I would REALLY like to see happen, VERY soon: so many of the deaths marked under the “cause of death: COVID 19″ were discovered” to be signficant;ly inflated by marking down EVERYONE who had a positive blood test for the virus as BECAUSE of….. even if they showed up at hospital in an ambulance, massive heart attack in progress, or came in to the ER with a gunshot wound to the head, then died before morning… and happened to have this virus in their bodies.

    With the “connexions” in place, I’m not even certain I can trust a report from the folks at Johns Hopkins to be fully truthful AND accurate. They get too much help from Bloomburg.

  23. If we would have just forced nursing home residents to stay in their rooms and take care of themselves, none of them would have died from COVID-19.

  24. Todays assault on reason: State governments will hire hundreds of thousands of “contact tracers”. No experience necessary, nothing useful to accomplish except political laws 1 & 2. 1 = DO SOMETHING. 2 = BAFFLE THEM WITH B.S

  25. Without being able to somewhat accurately identify and track the asymptomatic carriers who apparently make up somewhere between 35-60% of all people infected, how can any estimate, calculation or model come up with a credible transmission rate?

    1. Who cares?

    2. Absolutely right…
      More comically, it is amazing how many news stories will grant a huge number of asymptomatic cases exist relative to the clinical cases but then say, with alarm, “but there are still many people without anitbodies”!

  26. Who gives a shit? Lockdowns shouldn’t even be considered at this point.

    And these models should just be used as guides not as a means to end to form policy. Sure, you can lockdown but the trade-offs will be horrible.

    So deciding which models to use or root for is irrelevant, pointless and besides the point.

    I don’t profess to know what to do but I do know two things: One, the virus isn’t as lethal as first thought and seems to prey on a specific demographic and two, we tried lockdowns and the cost are simply too high.

    We have to live with it. Take precautionary measures as we learn more.

  27. Todays assault on reason: State governments will hire hundreds of thousands of “contact tracers

  28. We can only plan, how to overcome this crisis. But Its a sensitive issue, how we gonna deal with it is really challenging. The effects after lifting lockdown can cause more damage.

  29. The author doesn’t even explain how these models are affected by lockdowns or the lack of them. Yes, the trends might be changing, but how do lockdowns play into that?

    1. The author is a smart fellow, but does not know much math and most probably does not understand these models in the first place.

      I respect Sullum’s verbal reasoning, but when he talks about math related topics, he is out of his depth.

  30. So Texas loosened the lockdown, and the R barely changed… Is that change even significant? What’s the error bars on Gu’s model? (For that matter, what are the error bars on the Utah model?) Reporting numbers without some sense of error or significance should be journalistic malpractice.

    I don’t think either model really supports lockdowns. Ultimately, the only longterm solution is herd immunity. Lockdowns can’t be maintained for months without dire economic consequences that will be measured in bodies (and likely already can be). It’s a natural disaster, some people are going to die, and there’s nothing we can do about it. Shooting ourselves in the foot only makes it worse, not better.

    (Also, Gu’s model assumes homogeneous population mixing, which is both obviously false and relevant.)

  31. While I would prefer to believe the more optimistic scenario, the Gu model’s historical performance makes a compelling case for (relative) pessimism. rowlett electrician

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