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I want to do something on the first weeks of the zombie apocalypse. I am using a virusal, slow, infinite energy, 24 hours or so transformation time, zombie model. So I want to know, if let us say a zombie is created, or even 100, can a zombie apocalypse theoretically happen? Wouldn't the military work its way through? I am planning on doing it in a receding/increasing way, so first everything seems safe, and then a zombie is missed on the search and it manages to start again.

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    $\begingroup$ 'Biting' is a horribly inefficient transmission vector. It'd take some people...but as soon as folk figured out what was going on, it'd get shut down pretty quickly. Ref: cracked.com/… $\endgroup$ – guildsbounty Oct 15 '14 at 17:50
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    $\begingroup$ Welcome to worldbuilding :) Are your zombies visibly different from uninfected humans? I can imagine it spreading, maybe, if they stay looking human and remain intelligent with a drive to spread the infection. Knowing what intelligence level and appearance they have will help narrow down the answers. $\endgroup$ – trichoplax Oct 15 '14 at 18:17
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    $\begingroup$ xkcd.com/734 $\endgroup$ – Epiglottal Axolotl Oct 15 '14 at 18:38
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    $\begingroup$ It's just really hard to explain. Your best answer is to think about "what started it" and go from there. For example if it's a chemical everyone in the town was exposed to that caused them all to turn, that might work. Again the threat would be short lived but at least you can explain a whole town being taken over. $\endgroup$ – Tim B Oct 15 '14 at 20:02
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    $\begingroup$ Do you know why we have hunting seasons? To stop our people from driving every species in the woods to extinction. If we put open season on everything for a year there would be nothing left to hunt. Now imagine a decaying zombie trying to eat people. We wouldn't need the military to nip this in the but: just put open season on the infected. $\endgroup$ – JDSweetBeat Apr 22 '15 at 17:55
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The best way to do this is to make a differential equation and look at the result. Some people have done this before and it really isn't that difficult math. This paper does definitelly leave room for improvement. If you are learning differential equations or want to remember, I highly recommend trying to make a model that works for practice.

There is a probability of interaction between a zombie and human proportional to the number of zombies and humans in the close region.

For each interaction between a human and zombie, there is a probability of 1 human leaving (Ph for human wins), 1 zombie leaving (Pz for zombie wins), or 2 zombies leaving (Pc for conversion). This is dependant on alot of factors but lets say it is constant.

There is the potential for spontaneous birth and death but lets say that is negligible.

$$\frac{\partial Z}{\partial t} = CHZ(P_C-P_H)$$ $$\frac{\partial H}{\partial t} = CHZ(-P_Z-P_C)$$

As the probability for humans is only negative, it means that in short periods of time with any number zombies and humans, non-zero probabilities for conversion, and some interactions: Human will die from zombies. If the value of $P_C-P_H$ is negative, however, the number of zombies will decrease too. In most cases, this means that a small group of romero zombies would die out very quickly. In order for a zombie appocalypse to happen, you need some way to manipulate this such that $P_C>>P_H$ but not high enough such that all human die too quickly.

28 days later does this by increasing $P_C$ to high levels with vomiting blood and decreasing $P_H$ by setting it in largely gunless London. Walking dead does this by making everyone turn into zombies at any death to create a probability of spontaneous zombie / human conversion without invocing the $CHZ$ zombie human interaction parameter. This also effectively bypasses $P_H$.
If you look, i'm sure you can find a good way to do this too.

The best way to do this seems to be to innoculate the system. A massive number of zombies upfront will collapse society increasing the chance for victory for the zombies in each interaction (group zombie attacks and sickly underarmed humans). This is best done by adding incubation times, invisible carriers who spread it without other's knowing, or an environmental source which kills most upfront. This means that you can have $P_H>P_Z+P_C$ but have it look like a traditional zombie apocalypse.

You also realistically need to include the ability for sections of either group to isolate itself/group up as it increases the ability of the weaker to survive. Some implementation of birth/natural death/ human-human killings would improve it as well. I would also find it fun to include a cyclic "night time" in which zombies have the upperhand while humans do in the daytime.

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    $\begingroup$ "When simple mathematics answers a complex question, the mathematics is either ludicrously oversimplified, or a work of genius." $\endgroup$ – Salmoncrusher Aug 29 '16 at 15:49
  • $\begingroup$ @Salmoncrusher where is the quote from? I agree with the concept. This is a very oversimplified model but helps define concepts that are hard to describe without it. A complete model is not needed to draw some informative conclusions. This math is the work of genius... in other fields haphazardly applied to a fictional scenario. $\endgroup$ – kaine Aug 29 '16 at 15:59
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Unfortunately, zombie apocalypse scenarios run into a big problem with zombie propagation. Kaine already gave the simple version of the equations but note that there's a big problem here: Either the number of zombies goes up--and the humans are soon wiped out, or the number of zombies goes down--and the zombies are soon wiped out. In neither case do you end up with a zombie apocalypse scenario.

Besides, the equations assume humans were stamped out by a cookie cutter. To end up with an apocalypse scenario you need to look at humans in a more complex fashion:

You have your average city dweller. Few have much combat capability, Ph will be low, Pc will be high. The zombie "virus" will spread through them like wildfire unless the infection cycle is too slow. For zombies like we saw in the World War Z movie you'll get near total conversion very quickly.

You have some combat-capable city dwellers. Unless they are lucky to realize what's up in time and find someplace zombie-proof to hole up they aren't going to fare better but they'll thin the herd a bit before going down. While their Ph is high they will face so many encounters the numbers will get them in the end.

Finally, you have the country dwellers. The population density is much lower which means prepared individuals won't have nearly the threat of being swarmed and both firearms and the skill to use them are much more widespread. The lower population density also means more time for a warning. Ph is high and they won't be swarmed.

This latter group is the only path I see to an apocalypse scenario. Much of the world becomes fully converted, the survivors are mostly farmers and ranchers.

There is also the approach used in John Ringo's zombie novels--the zombie virus piggy-backs on a flu virus. (Some lunatic's genetic engineering.) The flu spreads like flu always does (especially when the lunatic places dispensers in places like airports), the disease is pandemic before anyone realizes it's more than just a nasty strain of flu. With so many infected at the start society collapses before the government gets it's act together. Since his zombies aren't actually undead they don't meet the parameters you set out, though.

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  • $\begingroup$ There's also Andrei Kruz novels where virus actually boosts one's immunity and in small doses is generally beneficial, except for side-effects in recently dead flesh. Disease becomes pandemic before anyone actually realises that there is a disease. $\endgroup$ – Daerdemandt Sep 5 '16 at 19:04

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