The coronavirus illustrates evolution on action


The pandemic has given us a crash course on evolution. Evolution deniers must be having a hard time explaining away the evolution-suffused news dealing with mutations, growth rates, and the like. But it also provides an opportunity to explain some of the mathematics of the phenomenon.

You would think that if a mutation had a slight advantage over its predecessor, then it would over time grow in size relative to the other but the older one would still be around. But that is not what happens. We see how some new variant, if it has some advantage over its competitors such as greater transmissibility, rapidly becomes dominant in the population, pushing the previously dominant ones into the background.

This graph shows the different peaks due to the different variants at the current time.


In this graphic from the CDC, we see the rapid rise in the proportion of the Omicron variant (purple) compared to the previously dominant Delta (orange).

The virus population grows by infecting others. The relevant quantity is the doubling time. For Omicron it is about 2-3 days while that of Delta is 5-7 days. The difference may not seem large but when you are talking about doubling times (or exponential growth) small differences can give rise to large effects. It will not be long before the Delta becomes as negligible as the Alpha and earlier variants that it replaced (the black part in the above figure). It is the nature of exponential or power growth that if something has a smaller doubling time than another, then its numbers will quickly overtake the competitor even if the competitor has a head start in terms of time and numbers.

To see this, the number of viruses N as a function of the starting value No, doubling time T, and time t is given by N=2t/T. Let’s assume that the doubling time for Omicron is two days while that of Delta is five days. Suppose that at one point in time, the fraction of Omicron cases was just 0.1%, with 99.9% being Delta. In just 10 days, the numbers will be equal and in two months (60 days), Omicron will be 99.9% of the total, completely reversing the initial situation.

The exponential and power functions do not mess around.

The number of Omicron cases right now is soaring in the US. As of yesterday, the seven-day average was 2.1 million, breaking the previous record of 1.8 million set back on January 12th.

The good news is that hospitalization and death rates are not rising at the same pace, growing at a much lower rate. The rising number of cases is ascribed to the greater transmissibility of this variant. So why are hospitalizations not increasing as fast? One speculation is that Omicron does not cause as severe symptoms as the Delta, which would be good news.

But another theory is that it is as severe as Delta and that it also has a greater ability to evade the vaccines. That is bad news. The rising number of cases is ascribed to larger numbers of vaccinated people getting infected, the so-called breakthrough cases. The good news is that being vaccinated does seem to mitigate the effects of the virus, leading to milder symptoms and lower hospitalization rates.

Of course, the idea that Omicron causes as severe symptoms as Delta is bad news for the unvaccinated who have no protection against it.

Comments

  1. Amarnath says

    The greatest shortcoming of the human race is our inability to understand the exponential function. A.A. Bartlett

  2. brucegee1962 says

    I’ve been reading in articles about those on the front lines — doctors and nurses — that pretty much 100% of those coming in now with severe cases who need to be intubated (and are likely to die) are either unvaccinated, or have other severe health problems and complications. That sucks of course for those in the latter group, but is greatly reassuring to me personally. As for the unvaccinated who are the main ones doing the dying these days, I really couldn’t give a toss. I saw a poll that only 18% of them are even aware of the above info, but that’s on them (and Fox News, of course).

    The group we should all be collectively terrified about as a nation is the under-five unvaccinated population, and also the large population of unvaccinated 5-12 kids. Next week the elementary schools will be inexcusably re-opened, and I fear we’ll be seeing whole classes ending up in hospitals.

  3. sonofrojblake says

    Here’s my problem right now:

    The number of Omicron cases right now is soaring in the US. As of yesterday, the seven-day average was 2.1 million,

    One speculation is that Omicron does not cause as severe symptoms as the Delta

    How the FUCK is that second sentence in any way shape or form compatible with the first? If there are two MILLION people out there KNOWN to be ill with the new variant, how is anything to do with the symptoms “speculation”??? I appreciate there’s a tendency to caution among epidemiologists, but seriously, this disease has been around for two months now, there are literallly millions of sufferers, and we’re talking “speculation” about the symptoms still? This gives fuel to the conspiracy theorists, hoax-claimers, vaccine-deniers and so on.

    I do wish it would stop.

    Or someone could explain how those two sentences fit together.

    /rant.

    I appreciate the above is intemperate and demanding certainty where it may not be warranted, but fuck me am I sick of this pandemic and in particular situations where public science communication doesn’t step extremely hard on bullshit and instead equivocates and is pedantically correct. I feel like the time for “proper” scientific facts is passed, if it was ever here, and to use Michael Gove’s infamous words, “the public are sick of experts”. Time to tell them to just shut the fuck up and get vaccinated, wear a mask, or get fucked.

  4. garnetstar says

    @1, so true! I think that it’s because there is, in normal life, no case of anything growing (or reducing) exponentially, so no one is familiar with it. It’s like trying to be familiar with quantum mechanics in middle-sized, middle-speed, Newtonian surroundings.

    @3, you are wrong, there isn’t any discrepancy between the sentences. The two facts are that cases are increasing, but hospitalizations/deaths are not increasing as quickly. That Omicron inherently causes less bad symptoms than Delta is only one explanation of the facts.

    Another is that now, a majority of the population isn’t immune-naive. Even if antibodies from prior vaxxes/infections aren’t that good against Omicron, T-cell and B-cell function is still there, that wasn’t in uninfected people. All of this could produce the “less severe symptoms” that seem to be seen.

    Only when Omicron sweeps through a truly immunce-naive population, as @2 says, under 5 and 5 -- 12 kids who aren’t vaxxed or previously infected, will we know if this variant truly causes “less severe” symptoms inherently. And, even then, since the only truly immune-naive populations left seem to be children, they may experience fewer symptoms on that account.

    There won’t be any way to tell if O. *inherently* causes less sever symptoms that Delta and the others, until O. can go through an immune-naive population of all ages.

  5. Reginald Selkirk says

    @3: How the FUCK is that second sentence in any way shape or form compatible with the first? If there are two MILLION people out there KNOWN to be ill with the new variant, how is anything to do with the symptoms “speculation”???

    I do not see any imcompatibility. The first sentence was about the number of people infected. The second sentence is about how severely ill infected people are likely to become.
    And it may take time for the severity to become apparent. You don’t get a positive test one day and they rush you into the ICU to intubate you. A positive test gets you isolation. If treatments are available they may be administered at this point (Paxlovid and Molnupiravir would be good for this, but are not yet widely available). It is only when the patient becomes very sick, as manifested in dangerously high fever, difficulty breathing, or low oxygen levels that they would get to an ICU.

  6. Reginald Selkirk says

    Things your simplistic model does not take into account:
    1) Mutants may compete with each other. I have seen speculation that a case of Omicron would prevent you from getting Delta. I don’t know if this is confirmed yet. I wouldn’t want to be the person who gets infected with both Delta and Omicron simultaneously though.
    Study: Omicron antibodies may block Delta variant infection
    2) A more infectious variant might expand the population of people who become infected.

  7. Reginald Selkirk says

    @1: People do pretty poorly with probability and statistics in general. Look at how many people gamble.

  8. xohjoh2n says

    @3:

    If there are two MILLION people out there KNOWN to be ill with the new variant, how is anything to do with the symptoms “speculation”???

    It takes up to a couple of weeks from exposure to symptoms.

    If it’s going to kill you, it’ll probably take up to a couple of weeks from there.

    If you’re going to survive, but suffer long-term effects, that might not be fully realised until a few months later.

    Omicron was reported on 24th November. It takes a bit of time to figure out just what a variant-specific testing regime *is*, then some time to roll that out globally. (And it looks to me as if that was done phenomenally quickly, but it still takes time.)

    Once you have a specific testing regime, then as cases progress you’ve got to gather the data (and -- a test result is relatively easy to acquire and sum up, but we need symptom reports on top which is more work and may not be gathered for all individuals), report it centrally, collate it, then figure out what it actually means. (Including deciding whether you yet have enough statistical power to decide that it means anything at all.)

    At the start of the spread, there just aren’t many cases to work with. Exponential growth, especially with a shorter doubling time, can get you big numbers very quickly, but you still have that initial ramp-up where there just isn’t enough going on.

    Furthermore, of those “two MILLION people out there KNOWN to be ill with the new variant” I’ll bet only a small number are confirmed PCR results of a type that can identify the specific variant. A majority are likely self-reported LFT results, where both the pattern of spread and a statistically valid sub-sampling using PCR strongly support the conclusion that the majority of those cases *must* be the new variant. But we’re not talking individual for-sure testing of each one of those.

    So, over the last couple of weeks we’ve started to get tentative suggestions about the severity of this disease variant, and those statements appear to be getting firmer. That to me looks like pretty much exactly the schedule you should expect to see.

  9. mnb0 says

    “Evolution deniers must be having a hard time”
    You keep on underestimating them. This is just variation within a kind, MS. The virus still is a virus and will always remain a virus, just like the fox always remains a fox, the goose remains a goose and the tiger will retain the character of a tiger (this reference is deliberate). Show me a virus turning into an elephant, then we’re talking. If corona shows evolution then it still ain’t Darwinian evolution. Either you lose or creacrap wins.
    I wrote this without consulting any creacrap page.

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