Also, it is important to explain what antibiotics are for and how to use them, and there will probably be language barriers. Literacy in these regions tends to be below 50%, and presumably the rural regions which most need the antibiotics also have the lowest literacy rates...
Even if each course of antibiotics bought and distributed has only a 0.1% chance of saving someone’s life, if you can get the antibiotics for $1/course someplace cheap (and not spend too much money travelling around distributing them) that’s still $1000/life—pretty respectable impact/$. And that’s a pretty conservative estimate...
The simple first-pass answer is to not measure impact, and just operate entirely on priors.
A very important question to ask here is: Is giving random people random antibiotics even positive EV? Just off the top of my head, here are some things that might happen:
People might steal them from one another, including at the risk of violence.
People might not trust the foreigner giving out random packs of stuff and throw them away.
People definitely won’t understand the foreigner giving out random packs of stuff, due to the language barrier.
People might take the antibiotics at the first opportunity, irrespective of whether they’re ill. That would likely result in negative EV (depending on which fraction of the population has antibiotics-treatable infections), e.g. antibiotics side effects. E.g. I imagine digestion problems are not good for people with malnutrition. If you save 1/1000 people and give the rest a week of antibiotics side effects, that can very easily sum to negative EV.
People definitely wouldn’t consistently take antibiotics as they’re prescribed by doctors, i.e. “take X tablets per day for 1-2 weeks”. How does that affect the EV? Suppose you’re infected and take antibiotics intermittently, or only for a few days. Is that even positive EV? What if people share the antibiotics and everyone only gets one tablet? (EDIT: And how bad is it to overdose on antibiotics?)
Do random antibiotics even work against random infections? <-> How do doctors decide what antibiotics to prescribe, and when?
And so on.
(And separately, as mentioned elsewhere: In a Malthusian equilibrium, why would you expect to save anyone by healing their infection?)
A very important question to ask here is: Is giving random people random antibiotics even positive EV? Just off the top of my head, here are some things that might happen:
People might steal them from one another, including at the risk of violence.
People might not trust the foreigner giving out random packs of stuff and throw them away.
People definitely won’t understand the foreigner giving out random packs of stuff, due to the language barrier.
People might take the antibiotics at the first opportunity, irrespective of whether they’re ill. That would likely result in negative EV (depending on which fraction of the population has antibiotics-treatable infections), e.g. antibiotics side effects. E.g. I imagine digestion problems are not good for people with malnutrition. If you save 1/1000 people and give the rest a week of antibiotics side effects, that can very easily sum to negative EV.
People definitely wouldn’t consistently take antibiotics as they’re prescribed by doctors, i.e. “take X tablets per day for 1-2 weeks”. How does that affect the EV? Suppose you’re infected and take antibiotics intermittently, or only for a few days. Is that even positive EV? What if people share the antibiotics and everyone only gets one tablet? (EDIT: And how bad is it to overdose on antibiotics?)
Do random antibiotics even work against random infections? <-> How do doctors decide what antibiotics to prescribe, and when?
And so on.
(And separately, as mentioned elsewhere: In a Malthusian equilibrium, why would you expect to save anyone by healing their infection?)