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I'm trying to model SARS-CoV-2 disease progression in individuals (and have very little background in biology).

At first glance, data from the literature on the duration and number of replication cycles that the virus undergoes over the course of a characteristic infection and the observed real world data on duration of an infection seem contradictory.

In The total number and mass of SARS-CoV-2 virions it was estimated that the virus undergoes 3-7 replication cycles over the course of a typical infection, and in SARS-CoV-2 by the numbers the duration of a replication cycle was taken to be 10hrs.

From this I would expect an infection to last 30-70 hrs (plus the time for the last virions to die out) which roughly is at most 4 days.

However, the median time from onset to clinical recovery for mild cases is around 2 weeks. In more severe cases it can take the patient up to 6 weeks to recover.

What causes this discrepancy? Is it that symptoms are (partly) caused by our immune system's response to the infection, not directly by the virus itself? In severe cases lasting up to 6 weeks, would one still expect only 3-7 replication cycles?

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The estimates you refer to seem to be of the "Fermi problem" variety - that is, these are "order of magnitude"-style estimates.

There's also the issue that they are talking about "typical" cases, whereas it seems you are talking about more extreme cases. I'm not sure where your estimate of "median time from onset to clinical recovery for mild cases is around 2 weeks" comes from but I suspect you may be referring to something based on hospitalized cases or something similar; the vast majority of COVID-19 cases do not involve hospitalization. There's also no reason to expect that time course of symptoms, which primarily involve activation of the immune system, need relate closely to the time course of viral presence.

In summary, though, when you are doing Fermi estimation, at the very most precise you might expect your estimate to be off by an order of magnitude. That means that, for this type of approach, 4 days and 40 days are the same number. In the first paper you link, note the precision of some of the numbers they are using to estimate:

~10–100 infectious units per cell

3×105–3×108 infectious units produced

You can't expect to get more precise when you're starting with estimates that vary over 1-3 orders of magnitude.

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  • $\begingroup$ very helpful, thank you for your answer! $\endgroup$
    – Vadim
    Commented Jul 20, 2022 at 16:01
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    $\begingroup$ This is a great answer, and I think this point is key: There's also no reason to expect that time course of symptoms, which primarily involve activation of the immune system, need relate closely to the time course of viral presence. The period of immune activation does not necessarily stop when the offending pathogen is cleared. $\endgroup$
    – acvill
    Commented Jul 20, 2022 at 16:55
  • $\begingroup$ @acvill This is so interesting - so you can be really sick despite your viral load being virtually nonexistent? What exactly is going on in the body? One guess would be that it has to recover from the lung tissue scarring caused by the virus $\endgroup$
    – Vadim
    Commented Jul 21, 2022 at 11:42

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