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last edit for tonight (heh)
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famulare committed Mar 23, 2024
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Expand Up @@ -88,9 +88,9 @@ This is exactly as it should be! At the maximum titer, every infected cell, sta

I want to reiterate again how awesome this is. From models of data about the probability people will get big, obvious polio infections, and from models of data about how peoples' immune systems respond---coarse models of organism-sized things---we've been able to derive how both are governed by what happens at the level of a single virus interacting with a single cell and the neutralizing antibodies perfusing the interstitial space immediately around that cell.

Furthermore, the macroscopic, person-scale models are remarkably simple. The immune response model is a simple, continuous function that holds across the entire range of achieveable antibody-mediated immunity. From the first infection in a completely naive person, to the highest possible memory response. All of the enormous complexity of the antibody-mediated immune system exists to do one simple thing defined in Equation (2)--linearly increase your neutralizing antibody response in proportion to how much you already have and how much pathogen gets through it.
Furthermore, the macroscopic, person-scale models are remarkably simple. The immune response model is a simple, continuous function that holds across the entire range of achieveable antibody-mediated immunity. From the first infection in a completely naive person, to the highest possible memory response. All of the enormous complexity of the antibody-mediated immune system exists to do one simple thing defined in Equation (2)--linearly increase your neutralizing antibody response in proportion to how much you already have and how much pathogen gets through it. And susceptibility is all about the dose, and how much of that dose gets through the immunity. And the complex physics reduces to simple, first-order chemical kinetics with a fudge factor for how getting antibodies and viruses to run into each other is hard (sub-diffusive).

And, as I argued in the [last post](https://famulare.github.io/2024/03/07/Conjecture-the-maximum-NAb-titer.html), this appears to be fairly universal for acute viral infections in people. As shown in Equation (4), the max titer is only a function of how antibodies transport through tissue (represented by the $\gamma$ and discussed in [the first post](https://famulare.github.io/2024/01/12/Two-fun-inferences-about-neutralizing-antibodies-and-viral-infection.html) and the maximum achieveable active dose (particles + infectiousness or antigenicity in the case of an inert vaccine) at the scale of a single cell and the immediately surrounding extracellular environment.
And, as I argued in the [last post](https://famulare.github.io/2024/03/07/Conjecture-the-maximum-NAb-titer.html), this appears to be fairly universal for acute viral infections in people. As shown in Equation (4), the max titer is only a function of how antibodies transport through tissue (represented by the $\gamma$ and discussed in [the first post](https://famulare.github.io/2024/01/12/Two-fun-inferences-about-neutralizing-antibodies-and-viral-infection.html) and the maximum achieveable active dose (particles + infectiousness or antigenicity in the case of an inert vaccine) at the scale of a single cell and the immediately surrounding extracellular environment and antibody trafficking through it.

# Next post
In the next post, I think I'll talk about how we can bravely over-interpret Equations (4) and (5) to better understand vaccine dose finding, see if we can understand conditions by which max titer can vary, and maybe say some stuff about what if antibodies were different sizes.
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