This is NOT Real Medical Data! But a simple model of disease progression may help us understand how to stay safer and explain to others. One of the tricks of of the actuarial approach is to emphasize good modeling and making reasonable assumptions even in the absence of much data. While that sounds glib, I think we can learn a lot from a thoughtful modeling approach even without a lot of specific data. This diary tests that thought. (Disclaimer: I am not an actuary, although I was raised in one of their dens)
Stylized Assumptions: Let’s assume a virus, a hypothetical one, but you can use your imagination for applicability. Let’s also assume that unvaccinated people (labelled “No Vax” in the charts) have a 3-day recognition lag before the body realizes that there’s a new virus present that needs an immune response. For simplicity, let’s assume a vaccinated or previously infected person (“Vax”) has a no such recognition lag, and their immune response starts gearing up immediately after initial exposure. However, let’s assume the body’s immune system needs about three days to spin up a full virus-fighting response once recognition occurs, either for vaxxed or unvaxxed people. We can call that the immune response lag. Let’s stipulate that this hypothetical virus doubles inside the body once every 1.5 days in the absence of an immune response. We can call that the virus’ doubling time. Finally, let’s assume that once the immune response gets its act in gear, it can kill about half of the virus present per day. That’s the kill rate. Of course, this vastly oversimplifies the stupendous complexity of real biological systems, but please follow on below the fold for some stylized implications…
The chart at the top shows some implications of the assumptions we’ve made. Let’s say this virus is deadly at 2000 “units” of viral load. The first key implication, at least based on our assumption of a doubling time of 1.5 days and a long recognition lag for the unvaxxed, is that eliminating the recognition lag by vaccination or previous infection really matters. In the chart below are two examples, a 100 unit and 150 unit “sudden” initial exposure, with or without recognition lag (labeled “Vax” vs. “No Vax”). The term “sudden” means a one-time exposure. That poor unvaxxed person suddenly exposed to 150 units (the yellow line in the chart) nearly dies in this model!
For most of us, the “sudden” one-time exposure chance is no longer our reality. Instead, we’re now swimming in virus on a daily basis.
Here’s another chart that compares people exposed not just once, but on a daily basis. Of course, given our assumptions about disease progression, a daily 100 unit exposure kills our unvaxxed patient! That guy flatlines at the deadly 2000 unit level just as the immune system is kicking in, but the kill rate isn’t high enough to counteract continuing exposure to ever more germ units each day. But vaxxed folks in this model, or people with lower daily exposures do OK. Even a daily 100 unit exposure seems survivable without the recognition lag, although it would probably be miserable to have a viral load of 600 units continuously! And, of course once exposed, even unvaxxed people would gradually develop a faster immune response over time, which we don’t try to model.
I feel like I’m the guy on the bottom orange line of the chart above: “Daily 25, Vax”. Working in retail, I feel like our family gets constant low level exposure. I haven’t had Covid yet. In fact I haven’t even had a bad headache and hardly any cold symptoms since the start of the pandemic.
It’s mostly luck, of course. But we’ve tried to reduce our recognition lag by getting vaccinated and boosted as soon as possible. I’ve been trying to reduce chances of large sudden exposures by not traveling more than necessary or spending a lot of time in restaurants or bars, and by wearing a N95 mask when I do have to spend time inside crowded places. We try to reduce daily exposure by monitoring the ventilation in our shop with a CO2 monitor. It helps that I’m not a huggy person in the first place. Finally, I’ve been trying to reduce my immune response lag by trying to get extra sleep, even though that greatly annoys my partner.
Bottom Line: I think Covid is best modeled as an analog system, not a digital system. It’s not a 0 or 1 — you either get exposed or not. Instead, it’s the degree of exposure that matters, either in one-time exposures or daily background exposure. And we can reduce our recognition and immune response lags, and bolster our immune system’s kill rates with some personal choices and annoying but effective social sacrifices.
These math-based model illustrations may be wrong. I would happily accept comments on how to improve the math or set different assumptions that might make the modeling more realistic. It’s not rocket science — for example, here’s how the spreadsheet looks for that “Sudden 100, No Vax” scenario. I find these sorts of modeling efforts helpful, and I think others might too. Of course, if real medical types think it’s so simplistic as to be misleading, let me know and I’ll delete!
Disease Progression |
Death |
Days |
Kill Rate |
Scenario |
Sudden 100, No Vax |
2000 |
1.5 |
0.5 |
Day |
Exposure |
Viral Load |
Doubling |
Immunity |
0 |
100 |
100 |
|
|
1 |
|
167 |
67 |
|
2 |
|
278 |
111 |
|
3 |
|
463 |
185 |
|
4 |
|
772 |
309 |
|
5 |
|
1,286 |
514 |
|
6 |
|
1,243 |
857 |
-900 |
7 |
|
1,022 |
829 |
-1,050 |
8 |
|
778 |
681 |
-925 |
9 |
|
567 |
518 |
-729 |
10 |
|
402 |
378 |
-542 |
11 |
|
280 |
268 |
-390 |
12 |
|
193 |
187 |
-274 |
13 |
|
131 |
128 |
-190 |
14 |
|
89 |
88 |
-130 |
15 |
|
60 |
59 |
-88 |
16 |
|
40 |
40 |
-60 |
17 |
|
27 |
27 |
-40 |
18 |
|
18 |
18 |
-27 |
19 |
|
12 |
12 |
-18 |
20 |
|
8 |
8 |
-12 |
21 |
|
5 |
5 |
-8 |
22 |
|
4 |
4 |
-5 |
23 |
|
2 |
2 |
-4 |
24 |
|
2 |
2 |
-2 |