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Comment by jbritton | Hacker News Reader

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.

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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.

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