I have been wondering about the effect of the degree of initial infection. I kind of assume the virus grows exponentially inside the body and would dwarf the initial constant. If a low initial dose affects the severity of the disease, I think that would be incredibly useful to know. I also wish there was info on percentage of infection via fomites vs inhalation.

I think it’s the opposite. The initial conditions have a profound effect on the exponential nature of the growth. Half the dose could mean that your immune system can suppress it. There is probably critical rate at which both growth rates match.

I don't think my response is 100% correct. The rate of change (derivative) of an exponetial function is another exponential function. d/dx(2^x) = (2^x)*ln(2). And if the base is e, then d/dx(e^x) = e^x.

Yo people, I don't understand why my statements are correct - please someone with a math background or an epidemiologist comment here, I suck at math and I don't understand how these growth rates compare. My comment is being upvoted but it may not be true.

Under the exponential growth model, the increased incubation time (before you hit the same total population size) is inversely proportional to the log of the initial dose, so (e.g.) 1/100th of the initial dose gives you only ~7 (log2(100) = 6.64) additional doubling times before arriving at the same population size. While this is not insignificant, it does mean that initial dose is potentially much less important than sources of variability that affect the in-host doubling time.

Edited to add: Here's a preprint that is relevant to the "initial dose vs. immune system response" thought: <https://www.medrxiv.org/content/10.1101/2020.03.26.20044487v...

The math is a simplification of a biological process that is highly variable and poorly documented. Your original idea is a fine hypothesis, though the suitability of the params behind exponential growth is mostly irrelevant.

We’re learning a lot about virology during this time. Infection and immunity are not binary, and now we have enough data to recognize that. We will also learn a lot about mutation, things like carrier recombination. I think this will change everything about how we attempt to control things through vaccination.

> I kind of assume the virus grows exponentially inside the body and would dwarf the initial constant.

That assumes your immune system wouldn't kick in during the asymptomatic phase or a time close to exiting the latter. But your immune system would actually kick in as soon as it detects the infection, which would plausibly be much earlier. That would effectively buying you time to figure out which antibodies to produce before things become out of control.

Variolation

"The procedure was most commonly carried out by inserting/rubbing powdered smallpox scabs or fluid from pustules into superficial scratches made in the skin. The patient would develop pustules identical to those caused by naturally occurring smallpox, usually producing a less severe disease than naturally acquired smallpox. "

https://en.wikipedia.org/wiki/Variolation

> I kind of assume the virus grows exponentially inside the body and would dwarf the initial constant.

Perhaps a more mild initial growth stage gives the immune system more time to respond.

If the immune response occurs in constant time, and is able to neutralize up to a constant number of viri at that engagement time, then you'd expect to see bimodal outcomes.

Most infectious diseases are dose dependent in their effects actually, which can be a bit counterintuitive. I dont know of any data for covid yet, but heres a paper on influenza, another viral disease:

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4342672/

In addition to the other comments, there's also thought to be differing impacts by infection location.

Covid in your alveoli is very bad. Covid in your throat not so much.

Not expert but I think if the initial constant can be several orders of magnitude different (I guess a few when airborne vs billions in a droplet) then it can impact the delay of the infection and give time for the immune response.

Yeah, as I understand it, typically the "dose" of the initial infection is important for how bad the symptoms will be.

The virus will grow exponentially, but so will the immune response, so starting conditions are important.

This is a basis for the old pre vaccine "variolation" strategy of getting immunity. Some radical thinkers argue for it as a Covid remedy.

Early on, there was some discussion of the possibility that folks whose initial exposure is via the eyes would have a more mild illness than if the exposure was via nostrils or inhalation, because the immune system would have time to begin work while the virus was multiplying more slowly in tissue less suited to it.

I haven't heard anything in weeks studying anything like this, though, so I don't know where we ended up, if, indeed anybody knows anything at all.

I remember one of the health experts in a Sam Harris podcast saying in an interview the dosage affects the severity and that this is seen in some other viruses (though I don't recall which ones). That's one reason doctors and nurses might be getting hit so hard, due to the continual exposure.

These were exactly the assumptions of the RIVM in the Netherlands end Februari and March causing it to completely spiral out of control.

> causing it to completely spiral out of control.

I live in the Netherlands and I think you could say that we actually have it quite under control (relatively speaking of course). We never reached peak ICU capacity and the ICU occupancy has been steadily declining for more than two weeks now[1]. Our schools for children between the ages of 4 and 12 are scheduled to partially open again on the 11th of may[2].

[1] https://nos.nl/artikel/2331720-coronacijfers-van-25-april-ri...

[2] https://nos.nl/artikel/2331460-kabinet-wil-basisscholen-voor...

We, the Netherlands, got it under control because we went into stricter lockdown against the advice of the RIVM. Above assumptions led to advice against a lockdown.

Only under pressure of the IC doctors on Sunday the 15th of march did the prime minister close all schools and restaurants. (A high school is like a festival every day)

The policy and advice of RIVM has been wrong and misleading from the end of February. For many of us it was already clear they lost control beginning of March.

There was one hero in the North of the Netherlands who went against RIVM and the Minister of health: https://eenvandaag.avrotros.nl/item/het-gelijk-van-microbiol....

This article in the Volkskrant describes how the RIVM was panicking beginning of March, but the prime minister wanted to present "good weather", and they also send their stock of masks to China beginning februari: https://www.volkskrant.nl/nieuws-achtergrond/nederland-stuur...

Even now they are not testing healthcare people with symptoms in elderly homes and also not providing any sort of masks. Claiming the available masks are not of sufficient quality, they prefer to send healthcare people to work without masks then to get high quality masks even if it is without the preferred certificate.

Last point. Under control is relative. The IC capacity reached a higher number then we ever anticipated, still more IC beds are occupied by corona patients then we had in total beginning of 2020. https://stichting-nice.nl/

For most of the hospitals in the Netherlands most operations and treatments are still postponed. For instance for many cancer patients the date of their treatment is still not sure: https://www.volkskrant.nl/nieuws-achtergrond/chemo-uitgestel...

The data doesn't support any of this. Overlaying the R0 estimation and the date that interventions were taken shows that the original "stay home when sick, wash hands and don't shake" advise had the biggest effect. This also matches most research that has been done on influenza. The lockdown on schools and restaurants had a much lower effect.https://www.volkskrant.nl/nieuws-achtergrond/corona-onder-co...

The RIVM lost the battle in Februari not in March, this is was what my initial comment referred to.

Throughout Februari and March they had the following policy:

- Clearly stating and assuming that asypmtomatic people cannot or are extremely unlikely to transmit (had letters sent to schools and events I particpated in, was also on their website). True or not, there was no data to backup this up and an assumption like this has big consequences when false.

- When from risk area AND with symptoms as a policy they didn't test. In general the whole focus was to test as minimal as possible. Causing us to be completely caught off guard of the true scope untill March.

- Clearly trying to sell the idea that masks don't work for normal people, while at the same time trying to claim them for themselves

- As a policy not testing healthcare people, not even with symptoms. First random test of healthcare people with symptoms in the south was only done on the 8th of march, they were shocked by result (and for a long time untill march allowing people to work with symptoms ). https://www.rivm.nl/nieuws/steekproef

- As a policy "non-essentials" healthcare people get no protection unless evidence of covid and hardly get tested. 900 of 2100 healthcare/elderly houses now have the virus with 20 to 30 percent death rate.

- Failed attempt of centralised buying of masks and other protection wear

https://www.volkskrant.nl/nieuws-achtergrond/jos-de-blok-buu...

- Till the end of Februari claiming they had it under control

- etc...

There is more things to point out but Ill leave it at this. The above assumptions and actions are a big part of what made the Dutch ministery fail to deal with the crisis properly and on time. Like many of the Western democracies. If they would have acted in Februari a full lockdown probably could have been prevented or shortened, lives would have been saved and many other treatments wouldn't have been cancelled or postponed.

The article i've linked to above talks about the doctor who did the opposite in the North, and was succesful with it, they even tried to force him to follow their policy.

To come back to your article. The short answer we don't have enough data (yet) to make such conclusions.

It seems reasonable that from the 9th of March the infection rate went down. This was the week all of Europe freaked out and many people started working from home, even if it wasnt official policy except for in the South of Holland (this idea was good, but too late). Certains schools already (partially) closed, partly because not enough teachers were showing up.

Whether or not school en restaurant closure lead to a lower infection rate is not clear from the data. The RIVM's analysis indeed suggests that it only had a small impact. The English analysis of the Dutch data in the same article does suggest a bigger impact. It's telling that the RIVM doesn't trust their own analysis enough to turn in into policy, you can watch the briefing of Dissel of last week, they only very slowly open the elementary schools in a few weeks from and don't open restaurants and high schools till the end of may.

> Rijksinstituut voor Volksgezondheid en Milieu

> Netherlands National Institute for Public Health and the Environment

> The Netherlands National Institute for Public Health and the Environment, is a Dutch research institute that is an independent agency of the Dutch Ministry of Health, Welfare and Sport. RIVM performs tasks to promote public health and a safe living environment by conducting research and collecting knowledge worldwide.

Where did you read that? Superficially that might make sense - less virus particles == less obvious symptoms - but there are a wide variety of virus responses that show virulence and infectiousness aren't necessarily correlated.

If anyone wants to read more about this I can't recommend highly enough the book Spillover by David Quammen, which was published in 2012, and covers zoonotic (animal-to-human transmission) viruses, including SARS. Reading the section on SARS made the hairs on the back of my neck stand up. It's uncannily similar to what's happening with Covid-19, and explains a lot of the background involved in these kinds of viruses.

A crude mathematical model from Swedish authorities on the Stockholm outbreak used two parameters: 1: the fraction of undetected cases (assumed to be mild or asymptomatic) and 2: the relative infectiousness of that group compared to the “detected” group.

The larger the undetected group is, the lower their relative infectiousness has to be in order to fit the observations. The best fit I believe was 1/25 detected and 11% infectiousness of the undetected group.

For the particular conditions in Stockholm, such as testing prevalence etc

Yes absolutely. The actual parameters would be different everywhere but they seem to indicate that the symptomatic group is more infectious (which I guess is the base hypothesis for a droplet transmitted disease).

Thanks - that's the kind of thing I was looking for, but this line stuck out to me: "However, the evidence of the relationship is limited by the poor quality of many of the studies, the retrospective nature of the studies, small sample sizes and the potential problem with selection bias." The book I mention gives me enough reason to doubt that what we know about Covid-19 at this point is anything like the whole story.

I actually do remember reading that this was true specifically in the case of COVID — that more exposure so far seems to correlate with a worse infection.

Sadly, I have no idea where I read this. But... I know I did! Recently! Maybe NYT?

This is the article you meant: https://www.nytimes.com/2020/04/01/opinion/coronavirus-viral...

Yeah, I saw it too. The hypothesis, as I recall, is that the more virions inhaled, the more likely some of them will get deep in the lungs where they can do the most damage.

I read something like that too. I came away thinking that ingestion might be a better way to get it than inhalation. I think you really need to keep it out of the lungs and nervous system. But that's all my impression from who knows where.

Bucheight

>> Also, many virologists mentioned in recent texts that the initial concentration of the virus you receive can affect how sick you'll get - the more viruses you're exposed to, the faster they can invade the body and the more severe it will get.

That is basic infections 101. When you are exposed to any dangerous virus a race starts between the virus and your immune system. If the virus starts out only infecting a handful of cells, your immune system has a head start in developing antibodies before symptomatic infection sets in. (This is also a basic principle behind many vaccines.) But if you are hit will a massive viral load that instantly infects every cell in your lungs, the immune system is fighting uphill from day one. A massive initial viral exposure can also trigger an excessive immune response, for instance dangerously high fever. Such an immune response can be as deadly as the virus. Much covid research is going into not defeating the virus directly but regulating/slowing the immune response to the patient survives their own immune response.

This principal explains why healthcare workers are suffering so. They are exposed to constant massive doses of virus, possibly from multiple patients carrying slight different versions of the virus. So they get sicker than people who are exposed in the general community.

Sleep deprivation and extreme stress could be factors that affect healthcare workers (1)

https://theconversation.com/coronavirus-does-the-amount-of-v...

There's already a comment above pointing out that it might be the initial infection location plays big role. Seems very likely that poor ventilation (in e.g. medical facilities) is main cause of severe cases.

Also, the virus is replicating exponentially only if it can reach many uninfected cells. It takes ~10 hours for an infected cell to start producing virus. Not sure whether non-specific immune system can somehow "contain" virus, would be great to learn about that.

I would think they'd be less infectious simply because they don't have symptoms that make them more so, namely coughing and sneezing and the like.

It depends. If you're not going to develop symptoms for another 14 days then yeah, you're not infectious. But for a few days before symptom onset you become just as infectious as you will be after symptom onset - which is one of the things that makes this virus hard to stop.

A low initial dose doesn't seem to affect the course of the infection much, though. For a sufficiently low dose either none of the viruses find an ACE2 receptor or your innate immune system wipes up the virus without you noticing (as it does for you with other viruses every day).

There's some evidence that particularly high doses can cause particularly bad prognoses. We have pretty good evidence that this is the case with measles. There's very anecdotal evidence suggesting that maybe this is the case with SARS-CoV-2. But it looks like low doses lead to a chance of no infection, not a chance of an asymptomatic one.

I'm very confused by this as I understand that asymptomatic patients are infectious. How does this square with your second sentence?

So, it looks like most asymptomatic infections later become infectious. Basically every person who gets symptoms had a multi-day asymptomatic infectious period they went through. SARS-CoV-2 does a better job than most of avoiding the automatic immune system because its large genome lets it encode a bunch of proteins that aren't for making new viruses but rather screwing with the immune system in ways that let it reach high numbers before the immune system catches on. Every virus that can actually make you sick does this but SARS-CoV-2 seems better than most. But frequently you're able to fight off the infection at a later point before the part of the automatic immune system reaction that makes you feel sick kicks into play but after you're got a chance to infect other people.

The normal course of the automatic immune system wiping out an invading pathogen without you noticing is that it happens immediately without you noticing and you never get a chance to infect anyone. But if that doesn't happen for COVID-19 or influenza or most things there'll be a time period after infection but before you notice anything where you're infectious. For COVID-19 this period is particularly infectious compared to the flu or SARS-1 or most things. It might be that flu and other coronaviruses tend to people who are infected enough to transmit the virus but never go on to develop symptoms. I don't know in that case.

WHO have maintained for months that asymptomatic patients are not infectious.

Until very recently they still said

"The risk of catching COVID-19 from someone with no symptoms at all is very low."

They now say "Some reports have indicated that people with no symptoms can transmit the virus. It is not yet known how often it happens. WHO is assessing ongoing research on the topic and will continue to share updated findings."

Yes, the WHO was incorrectly relying upon information provided by China. Since then it has become an accepted fact that asymptomatic transmission of SARS-CoV-2 is not only occurring, but is one of the primary transmission vectors.

https://www.nejm.org/doi/full/10.1056/NEJMoa2008457

Prof. Dr. Drosten (inventor of Covid-19 test) said in the interview below that there is a study which shows asymptomatic adult shed as much virus as symptomatic ones. He also said there is no good study on how many viruses are shed by kids.

https://tvthek.orf.at/profile/Additional-Content/1670/Langfa...

I remember Robin Hanson [1] used the second fact to recommend "variolation", injecting everyone with a tiny amount of the virus so that they'll get the immunity without the sickness (making it a "natural vaccine").

[1] http://www.overcomingbias.com/2020/03/variolation-may-cut-co...

how do you ever make antibodies if you are perpetually asymptomatic though?

do you carry it forever? does it attack eventually?

what happens if you are an asymptomatic carrier and get a vax?

"Typhoid Mary" was an asymptomatic carrier of typhoid fever for at least 38 years.

https://en.wikipedia.org/wiki/Mary_Mallon

FWIW I think that article shows her infecting people for only 15 years (1900-1915), then being quarantined for a further 23.

The Wikipedia article doesn't cover everything. Reference for the sibling comment: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3959940/

That article has 1906 (her engagement as cook in the Warren household) to 1932 (her paralysis) as the period of her infection of others, assuming after her paralysis she didn't infect anyone else.

That's still not 38 years; it's not especially important a point - she infected others over at least 2 extended periods amounting to mor than a couple of decades in total.

It's interesting to me, I thought nih.gov was a scientific publication but at least one part of that document appears to be opinion asserted as fact (~"she never intended to abide by the conditions of her release").

> ... 1906 ... to 1932 ... as the period of her infection of others ... That's still not 38 years ...

I never stated that she infected others for 38 years. Being an asymptomatic carrier does not require continually infecting others, only that the carrier maintains the infection without showing symptoms. [1] Additionally, the NIH article isn't complete in listing likely infections, as evidenced by comparing it to the Wikipedia article. Nor does is state that she continued to infect others until her paralysis in 1932.

As for the 38 years, the Wikipedia article notes 1900 as the first known, likely infection of a family she worked for. Then, from the NIH article:

> A post mortem revealed that she shed Salmonella typhi bacteria from her gallstones ...

Her death (and, presumably, post mortem) was in 1938. "Bacterial shedding" [2] implies infection and, thus, being a carrier in 1938, though asymptomatic. I arrived at 38 years by considering her likely a carrier from 1900 to 1938.

[1] https://en.wikipedia.org/wiki/Asymptomatic_carrier

[2] https://www.google.com/search?q=bacterial+shedding

A post-mortem confirmed that her gallbladder was loaded with the bacteria that cause typhoid.

Wikipedia mentions that autopsy might not have been performed.

AFAIK asymptomatic means you show no symptoms but your body fights and creates antibodies just the same. Disclaimer: I'm not a doctor.