Hopefully this is the right forum for this question. Apologies if it isn't.
So: imagine we have 500 vampires, and a human population of 8,000,000,000. Every week, each vampire snacks on a human. Whenever a human is bitten, they turn into a vampire.
Under these simple circumstances, it takes 24 weeks (or slightly under) for the entire human population to become vampires.
I can do that much on my own. What I'm struggling with is increasing the complexity of the calculation.
For example, we assume the humans instantly turn into vampires, but what if it takes a day or two?
Are the human birth/death rates negligible over the estimated period, or would they affect the final result?
How do we account for vampires taking different lengths of time between feedings? (For example, if they get peckish after a week, but they NEED to eat at least once a month.)
How do we map the changes in human behaviour? (500 vampires would have no problem feeding, but once half the human population has been converted, the surviving humans are going to be significantly less agreeable.)
Given the last two factors, would there even be a risk of vampiric starvation before the humans all die out?
These are the factors I just can't get my head around. I haven't done serious maths in nearly a decade.
(For the sake of the scenario, assume animal blood is not a viable source - it has to be humans. And yes, I'm aware that means vampiric extinction eventually, but I'm concentrating on the human aspect.)
For context: I'm a short-story writer, and I'm trying to write a bit on the struggles of having a large vampire population.
But for that, I'd like something a bit more complex than the simplest formula possible: "[starting_population] * 2 ^ x", getting the exact week of extinction. That's not narratively satisfying.
So I'm not after a perfect answer (which is likely impossible, given the fictional nature of the question), just a much more intelligent estimate, even one with a slight range to the time of extinction.
If you know how to account for the factors I've provided, or even come up with any of your own, I welcome any help!
And again, sorry that this question is a bit vague. As I said, I'm mainly after an answer with some mathematical depth.
So: imagine we have 500 vampires, and a human population of 8,000,000,000. Every week, each vampire snacks on a human. Whenever a human is bitten, they turn into a vampire.
Under these simple circumstances, it takes 24 weeks (or slightly under) for the entire human population to become vampires.
I can do that much on my own. What I'm struggling with is increasing the complexity of the calculation.
For example, we assume the humans instantly turn into vampires, but what if it takes a day or two?
Are the human birth/death rates negligible over the estimated period, or would they affect the final result?
How do we account for vampires taking different lengths of time between feedings? (For example, if they get peckish after a week, but they NEED to eat at least once a month.)
How do we map the changes in human behaviour? (500 vampires would have no problem feeding, but once half the human population has been converted, the surviving humans are going to be significantly less agreeable.)
Given the last two factors, would there even be a risk of vampiric starvation before the humans all die out?
These are the factors I just can't get my head around. I haven't done serious maths in nearly a decade.
(For the sake of the scenario, assume animal blood is not a viable source - it has to be humans. And yes, I'm aware that means vampiric extinction eventually, but I'm concentrating on the human aspect.)
For context: I'm a short-story writer, and I'm trying to write a bit on the struggles of having a large vampire population.
But for that, I'd like something a bit more complex than the simplest formula possible: "[starting_population] * 2 ^ x", getting the exact week of extinction. That's not narratively satisfying.
So I'm not after a perfect answer (which is likely impossible, given the fictional nature of the question), just a much more intelligent estimate, even one with a slight range to the time of extinction.
If you know how to account for the factors I've provided, or even come up with any of your own, I welcome any help!
And again, sorry that this question is a bit vague. As I said, I'm mainly after an answer with some mathematical depth.
