What about the asymptomatic infected? edit: as in the people who got infected by breathing in spores

@Hi0401, are the asymptomatic infected themselves infectious? If not, that merely stretches the timeframe, but nothing changes in principle. If they are infectious, things happen faster.

yes they are contagious, the disease is airborne during the asymptomatic period

I just realized that your post says Patient Zero was a zombie on day one. Not sure if it was intentional for simplifying the answer, but I'll edit the question to make it clearer that he didn't start as a zombie.

@Hi0401, nothing of that matters. At best, it moves things a day or two, or requires a slightly higher r number to compensate. Once you get into Fibonacci growth, or exponential growth, you get a runaway effect until the victims run short and they become the limiting factor.

This math is wrong. Day 12 would only have 248,832 zombies. It's time^rate, not the other way around.

@PapaSolen'ya, time^rate would be polynominal growth, rate^time is exponential.

It's not exponential. With your equation there would be 5.64802792x10^219 zombies after 1 year. And if the rate was less than 1, then the number of zombies would decrease.

@PapaSolen'ya, read back on the reports on covid. Getting r below 1 was the big goal ...

r, the rate of infection, as we are using it, was not used to measure covid. Take a look at my answer. Flu has a rate of only 0.16-0.33 new infections/person/day. According to your equation, the number of infected people would decrease over time, even though new people are still being infected.

@o.m. I'm just saying that people might be more likely to catch the infection from an asymptomatic carrier than from a zombie, since people will run from the zombies.

@PapaSolen'ya, that would be true if the flu ceased to be infectious after one day.

How so? 0.33 new infections/day means Patient Zero would infect 1 person every 3 days. There's nothing implying that the victims stop being infectious.

@PapaSolen'ya, in my formula, I made the simplification that the zombie dies after one day. This may not be true, but if it is false the infection just spreads faster.

Your entire formula is flawed. It's not exponential.

@PapaSolen'ya, what about 4^t is not exponential?

I'm saying that the correct formula is not exponential. Your formula is exponential, which is why it's wrong.

@PapaSolen'ya, exponential growth is the proper model for the early stage of an epidemic, when there are many more uninfected than infected. Delays like incubation periods can be modelled by the choice of the constants.

Half of the assumptions that your formula is based on were never stated by OP.

There is nothing implying that the zombies die after only 1 day, and Patient Zero isn't a zombie until day ~ 6.5. If Patient Zero infected only 0.33 people per day, like the flu, then according to your equation, there would be ~1.8x10^-7 infected people by day 14, when there should be ~5. If Patient Zero infected 1 person per day, like measles, then according to your equation, there would be 1 infected person by day 14, when there should be ~56.

On closer examination, you were correct about the formula being exponential. The formula should be (1)(1+r)^t

This solves the problem that arises when r<=1. Your formula should be 5^t, not 4^t.