This feels a bit petty, since I don’t really disagree with any of your conclusions, but there are some mistakes in the mathematics here.
Let’s assume a fraction p of all antibiotics used are used in animals, and a fraction 1−p are used in humans. (In your example, p=0.75.)
Let’s also assume that antibiotics use in animals is k× as effective at causing a resistance burden in humans per unit antibiotics used. (In your main example, k=0.1.)
Then the total resistance burden in humans is given by B=(use in animals)×(burden from animal use)+(use in humans)×(burden from human use), which in algebraic terms is B=p×k+(1−p)×1=1+p(k−1).
The fraction of the total burden caused by animal use is then A=pkB. If p=0.75 and k=0.1, this is A=0.0750.325≈23%. So, quite a bit more than 7.5%.
If k=0.01 (use in animals is 1% as efficient at causing a resistance burden in humans), then A=0.00750.2575≈3%. If k=0.5, A=60%.
So the fraction of the human burden caused by animal use could be quite high even if the per-unit efficiency is quite low.
One comment: while all your caveats about simplified reasoning and so on are well-made and still apply, I would generally be surprised if you could substitute a number like this in your analysis with another number three times the size, without affecting anything else, such that you could make the substitution and leave the wording unchanged.
That is to say, if a contribution of 7.5% was “very significant and worth pursuing”, I’d expect a contribution of 23% to be extremely significant, and worth making a high (or near-top) priority.
Of course, that’s the result for 10%, and 10% is just a made-up number. But I think the general point stands.
Good point. I’m unsure what the best practise in editing previous comments is—I don’t want to change it so much that the subsequent comments don’t make sense to another reader. Clarified now by leaving in the original number that fits with the reasoning around it while keeping the correction in brackets.
I think it would also be worth keeping in mind how hard it is to make progress on each front. Given that there seems to be widespread non-therapeutic use of antibiotics for farmed animals, and that (I believe) most people have accepted that antibiotics should be used sparingly, I would be surprised if there were no “low-hanging fruits” there. This is not meant as a complete solution, but rather is an attempt to identify our “next best move”. I would believe that cheap in-farm diagnostic tools should now be within reach as well, or already existing.
Separately from this, I admit being confused about the nature of the question regarding the importance of dealing with over-use of antibiotics in farmed animals. My understanding is that we know that inter-species and horizontal gene transfers can occur, so is the question about knowing how much time it takes? I just don’t have a clear model of how I’m supposed to think about it. Should I think that we are in a sort of “race against bacteria” to innovate faster than they evolve? Why would a delay in transfer to humans be a crucial consideration? Is it that antibiotic innovation is mostly focused on humans? Is there such a thing as a human-taylored antibiotic vs. farmed animal antibiotic? I suppose not? I cannot wrap my head around the idea that this delay in transmission to humans is important. So I guess I’m not thinking about it right?
[Added later:] Maybe the point is that if some very resistant strain emerges in a farmed animal species, we have time to develop a counter-measure before it jumps to humans?
This feels a bit petty, since I don’t really disagree with any of your conclusions, but there are some mistakes in the mathematics here.
Let’s assume a fraction p of all antibiotics used are used in animals, and a fraction 1−p are used in humans. (In your example, p=0.75.)
Let’s also assume that antibiotics use in animals is k× as effective at causing a resistance burden in humans per unit antibiotics used. (In your main example, k=0.1.)
Then the total resistance burden in humans is given by B=(use in animals)×(burden from animal use)+(use in humans)×(burden from human use), which in algebraic terms is B=p×k+(1−p)×1=1+p(k−1).
The fraction of the total burden caused by animal use is then A=pkB. If p=0.75 and k=0.1, this is A=0.0750.325≈23%. So, quite a bit more than 7.5%.
If k=0.01 (use in animals is 1% as efficient at causing a resistance burden in humans), then A=0.00750.2575≈3%. If k=0.5, A=60%.
So the fraction of the human burden caused by animal use could be quite high even if the per-unit efficiency is quite low.
That was sloppy of me, thanks a lot for the correction! Edited in the comment.
Cool, thanks.
One comment: while all your caveats about simplified reasoning and so on are well-made and still apply, I would generally be surprised if you could substitute a number like this in your analysis with another number three times the size, without affecting anything else, such that you could make the substitution and leave the wording unchanged.
That is to say, if a contribution of 7.5% was “very significant and worth pursuing”, I’d expect a contribution of 23% to be extremely significant, and worth making a high (or near-top) priority.
Of course, that’s the result for 10%, and 10% is just a made-up number. But I think the general point stands.
Good point. I’m unsure what the best practise in editing previous comments is—I don’t want to change it so much that the subsequent comments don’t make sense to another reader. Clarified now by leaving in the original number that fits with the reasoning around it while keeping the correction in brackets.
I think it would also be worth keeping in mind how hard it is to make progress on each front. Given that there seems to be widespread non-therapeutic use of antibiotics for farmed animals, and that (I believe) most people have accepted that antibiotics should be used sparingly, I would be surprised if there were no “low-hanging fruits” there. This is not meant as a complete solution, but rather is an attempt to identify our “next best move”. I would believe that cheap in-farm diagnostic tools should now be within reach as well, or already existing.
Separately from this, I admit being confused about the nature of the question regarding the importance of dealing with over-use of antibiotics in farmed animals. My understanding is that we know that inter-species and horizontal gene transfers can occur, so is the question about knowing how much time it takes? I just don’t have a clear model of how I’m supposed to think about it. Should I think that we are in a sort of “race against bacteria” to innovate faster than they evolve? Why would a delay in transfer to humans be a crucial consideration? Is it that antibiotic innovation is mostly focused on humans? Is there such a thing as a human-taylored antibiotic vs. farmed animal antibiotic? I suppose not? I cannot wrap my head around the idea that this delay in transmission to humans is important. So I guess I’m not thinking about it right?
[Added later:] Maybe the point is that if some very resistant strain emerges in a farmed animal species, we have time to develop a counter-measure before it jumps to humans?