When Zombies Attack!

[Stuart]

This The following mathematical analysis of a Zombie attack on the human race was published by the Carleton University, Ottawa. The conclusions are very interesting indeed and suggest that prompt, decisive and violent counter-action is the only possible response to a zombie infection if the human race is to survive.

[General Zod]

Which is pretty much something we've known since the first zombie films were made?

[Simon_Jester]

Yeah. Most of their analysis can be summarized as "if zombies are allowed to turn the uninfected into more zombies, with no effort made to reduce zombie populations, we're screwed."

To be fair, to the best of my knowledge nobody actually sat down and tried to do the differential equations to prove it, but it's not a surprising result by any means.

[Lagmonster]

It was actually a combo project with young men (duh!) from both the U of Ottawa and Carleton, the two universities in my town. It's silly, but it's fun to read for the attempt at seriousness it provides the subject.

[Steel]

While this is a good mathematical treatment of the subject, and their analysis in the SIR compartmental model framework is sound, I think they've made some fairly useless base assumptions in their model.

SIR models are pretty standard in mathematical epidemiology, and making a SZR model is something I did briefly for fun a while ago. Their model assumes that zombies can come from the dead whether or not they were killed by a zombie. The most ridiculous thing about their model is that zombies are created from the dead pile at rate <zeta>*R, but zombies are put into the removed class after they are defeated and then go straight back to being a zombie, so OF COURSE if there is a single zombie then basically everyone becomes a zombie as (Z+R) cannot decrease! Also, cryptic infection (where some are infected, but not symptomatic and can infect others during this time) is common in plants and in human diseases (eg HIV) but with zombies you dont get infected people infecting others till they go all braaaains, so that shouldnt make a contribution to the model.

A better model is to have SZRD, where D is destroyed and gone for good, so natural causes can contribute to the R category, or ignore it entirely if the situation does not have a significant source of fatalities aside from zombie hordes.

Another possible extension is to add a M class, military, who have a vastly higher probability of killing a zombie in an encounter, and are fed from civilians to represent the general population getting a clue and arming up and being able to defeat the zombies better.

My model, C(ivilian)ZMD(estroyed) showed the zombies were buggered in most reasonable scenarios. I'll post some stuff later if people are interested, but I'm pretty busy for a couple of days.

[Oni Koneko Damien]

Their model assumes that zombies can come from the dead whether or not they were killed by a zombie.

Also, cryptic infection (where some are infected, but not symptomatic and can infect others during this time) is common in plants and in human diseases (eg HIV) but with zombies you dont get infected people infecting others till they go all braaaains, so that shouldnt make a contribution to the model.

Wait... did you just try to claim that some 'facts' about zombies are true and some are not true? Umm... these are zombies we're talking about. Fictional creatures. If they wanted to include the 'fact' that zombies can fly and shoot laser beams in their study, they still wouldn't be wrong because they're dealing with an entirely hypothetical concept here.

As for zombies returning from the dead and cryptic infection, I read a book recently (Paroxysm) that had an interesting concept for dealing with this. Basically the zombiebug had two components: A virus which attacked and shut down the immune system, but could only be spread through fluidic contact, and an airborne bacteria that contains unexplainable 'necrochondria' which reanimates the body and severs the higher brain's control over it. Basically as soon as the bug hits, everyone's 'infected', but show no signs because their immune systems fight off the bacterial portion of it. If they get bit, the virus destroys the immune system and the bacteria reanimates them, but if they die of natural causes, then their immune system shuts down and, once again, the bacteria reanimates them.

As for the global death thingie, I've always considered it highly likely. It's a given that zombies in almost all popular forms suck quite horribly against any military force. But in a spreading-global-infection scenario, a vast majority of the time they won't be going against the military, but rather normal people who can easily fall to a shambling mob, and then get added tothe mob's numbers. Also take into account the massive rioting that's likely to take place when news of zombie attacks get out, the large number of paranoid wingnuts tying up military resources with attempts at armed secession in the confusion, and any number of random crime, racial/religious violence, etc. that's certain to go through the roof when people believe the movie-set precedent that this is the end of the world.

Sure, the military will easily steamroll any zombies it comes across. The problem is that the military can't be everywhere it's not, and for every group of zombies it annihilates, ten other groups will be spreading infection against riot and crime-torn populaces unfit to deal with them, and eventually the only living people left on the world would be the military and those few it is able/willing to protect. So maybe not a complete human extinction event, but enough of one that the world population is reduced to a tiny fraction of its original size with rather dim prospects for the future.

[Samuel]

Fictional creatures. If they wanted to include the 'fact' that zombies can fly and shoot laser beams in their study, they still wouldn't be wrong because they're dealing with an entirely hypothetical concept here.

Zombies are pretty well defined monsters. If you want to say "our zombies are different" call them vampires or make a new name. Word mean thing dammit!

but if they die of natural causes, then their immune system shuts down and, once again, the bacteria reanimates them.

Great. And what happens when the muscles are gone or people who have seen zombie movies burn the bodies?

a vast majority of the time they won't be going against the military, but rather normal people who can easily fall to a shambling mob,

I can walk faster than the zombies can and can defeat them with ladders, cars or other simple things.

Also take into account the massive rioting that's likely to take place when news of zombie attacks get out, the large number of paranoid wingnuts tying up military resources with attempts at armed secession in the confusion, and any number of random crime, racial/religious violence, etc.

In cases of invasion, people stick to their leaders. I doubt insanity will break out as the nuts won't have the protection of the state.

[General Zod]

Zombies are pretty well defined monsters. If you want to say "our zombies are different" call them vampires or make a new name. Word mean thing dammit!

Just like vampires are well defined despite people giving them new abilities and tricks all the time right? Oh wait.

I can walk faster than the zombies can and can defeat them with ladders, cars or other simple things.

Unless they're Dawn of the Dead style zombies. . .or 28 Days Later-style infected.

In cases of invasion, people stick to their leaders. I doubt insanity will break out as the nuts won't have the protection of the state.

I'd almost be counting on widespread panic at a minimum as soon as people realize monsters they used to think were fictional are attacking them.

[FireNexus]

This The following mathematical analysis of a Zombie attack on the human race was published by the Carleton University, Ottawa. The conclusions are very interesting indeed and suggest that prompt, decisive and violent counter-action is the only possible response to a zombie infection if the human race is to survive.

Since this is kind of your job, Stuart, how would you plan the zombie counteroffensive? I don't think I'm the only one who finds it fascinating to see you describe how to win wars.

[Dooey Jo]

"As clearly outlined in our fanfic, zombies which cannot be stopped will doom humanity."

Even if we assume that, say, decapitated (or atomized) zombies can come back to life, they would have no way of spreading the infection, since they have no mouth, and even if they could, they would probably be pretty useless, since they don't have a fucking head. Putting "defeated" zombies back into the zombie spawn pool makes no sense at all, even if you say "LOL zombies aren't real". The only reason they did it was to simplify the model, or in other words, assume perfectly spherical zombies in a vacuum.

[Simon_Jester]

Wait... did you just try to claim that some 'facts' about zombies are true and some are not true? Umm... these are zombies we're talking about. Fictional creatures. If they wanted to include the 'fact' that zombies can fly and shoot laser beams in their study, they still wouldn't be wrong because they're dealing with an entirely hypothetical concept here.

Yes, but if they're trying to analyze the classical movie zombie concept, it's generally agreed that it is at least physically possible to destroy a zombie such that it can no longer harm anyone. A mathematical model that does not allow for this possibility is going to produce unusually effective zombies, because you can't put the model's zombies down permanently even by dropping them into a blast furnace. Sooner or later, invincible zombies will get you no matter what you do.

[Oni Koneko Damien]

Zombies are pretty well defined monsters. If you want to say "our zombies are different" call them vampires or make a new name. Word mean thing dammit!

Actually zombies are pretty poorly defined. The only thing they all have in common is that they're 'dead', and even that's debatable if you include 28 Days Later. Depending on your source zombies can be slow, fast, die to head shots, spine-shots, heart shots, or full body incapacitation, come from infection, magic, radiation, space dust or biblical prophecy, rise from the graves, come out of hospitals, or under the thrall of magicians/necromancers/parasites/alien overlords. Depending on the source, infection can last anywhere from a few seconds to several days, preferred food may consist of brains, any fleshy bit of the body, bones or more obscure things, food may actually nourish the zombie or sit inert in their gastrointestinal tract, zombies can be little more than machines, show insectile intelligence, or show slight learning and problem-solving capabilities, zombies either decay over a short period of time, remain indefinitely preserved, or mutate further, they can be pitifully weak, human strength, or even superhuman strength. Again, all depending on the source.

I think the simplest definition that covers most all classical representation of 'zombie' is "A formerly human monster whose danger lies in its large numbers and ability to convert those it attacks into more of itself."

Great. And what happens when the muscles are gone or people who have seen zombie movies burn the bodies?

And this means... what exactly? Muscle decay is a problem that confronts all zombies, not just this version so it's not much of a criticism. And so some people burn the bodies. Some don't find the bodies until it's too late. Some simply don't know yet. Some refuse for religious/political reasons, denial, or just outright psychosis. Some are just too scared to touch it. You're expecting a bunch of semi-sentient savages to act with reason and forethought here.

I can walk faster than the zombies can and can defeat them with ladders, cars or other simple things.

How do you know you can walk faster? Did I ever list their speed? In this novel it's actually pretty inconsistent. Some shamble slowly, some can lurch along pretty well, some can outright sprint indefinitely. No one knows for sure what dictates a zombie's cruising speed. You seem to be pretty confident in yourself as well. Can you be sure you'll get perfectly lucky one hundred percent of the time? That you won't get bitten by any under any circumstances? That a drop of blood won't fly into your eye when you bash them over the head? That you'll remain perfectly rational and calm no matter what and not panic and do something stupid under any circumstances? That you'll be safe when you sleep.

And even if you do all of the above, what guarantee do you have that the average twit on the street will be approaching the problem with the same level of rationality?

[quoteIn cases of invasion, people stick to their leaders. I doubt insanity will break out as the nuts won't have the protection of the state.[/quote]

Right now we are on the verge of armed protests because of fucking HEALTH CARE. Do you really think everyone's going to remain calm and do what the TV tells them to when they find out one of their horror-movie staples has come to life (relatively speaking) and is walking among them? Recent events have proven that there are a disturbingly large number of nutcases out there seeking an excuse to go ballistic on society at large. Yeah, they're a minority, but what if a good deal of them use this as an excuse to go on mall shooting sprees? What if religious demagogues/gun nuts get on TV and tell people it's a liberal government conspiracy to take away people's freedom and that it's the responsibility of every true Christian to fight against this government intrusion in any way possible?

And once the nutcase minority acts up, the effects will filter through the more malleable sections of the mindless middle, and a good chunk could end up joining and following the nutcases, starting a vicious cycle. This isn't even taking into account what will be going on in countries that aren't as relatively stable as most of the first world is.

Basically the only way to ensure pacification is to declare martial law and enforce peace at gunpoint... in which case the nutcase minority will be immediately set off. And if that scenario comes to pass, exactly what point do you declare martial law? How bad does the spread of infection get before those in power decide their interests are better served by enforcing a curfew, shutting down borders and dealing with the possible panic and ensuing secession attempts rather that continuing to let infection spread?

[Simon_Jester]

Yeah, but this model's zombies are if anything more unkillable than even the most extreme ones in fiction, because they don't stay dead when you kill them. Even if you chop off their head and bury it under a crossroads or drop them into a blast furnace or dissolve the body in acid.

Defeated zombies go into a 'removed' pile, but it's a statistical certainty that anything in the 'removed' pile (ex-zombie or recently killed human) will eventually wind up a zombie (again). It's a serious flaw in their model, if you ask me.

[Oni Koneko Damien]

Yeah, but this model's zombies are if anything more unkillable than even the most extreme ones in fiction, because they don't stay dead when you kill them. Even if you chop off their head and bury it under a crossroads or drop them into a blast furnace or dissolve the body in acid.

Defeated zombies go into a 'removed' pile, but it's a statistical certainty that anything in the 'removed' pile (ex-zombie or recently killed human) will eventually wind up a zombie (again). It's a serious flaw in their model, if you ask me.

Well that is just plain stupid.

[Steel]

Yeah, but this model's zombies are if anything more unkillable than even the most extreme ones in fiction, because they don't stay dead when you kill them. Even if you chop off their head and bury it under a crossroads or drop them into a blast furnace or dissolve the body in acid.

Defeated zombies go into a 'removed' pile, but it's a statistical certainty that anything in the 'removed' pile (ex-zombie or recently killed human) will eventually wind up a zombie (again). It's a serious flaw in their model, if you ask me.

Well that is just plain stupid.

Indeed, that was my point in the first place.

On the cryptic infection point, even in your odd double pathogen scenario it still requires human zombie contact to turn the person into a zombie, and during the latent (infected but not symptomatic ie "It fucking bit me!") phase the person is not going to infect other people as they don't go biting them. Therefore the cryptic class isn't useful and actually harms the model (unless its 28 days later style "its in the blood" stuff and the population under scrutiny is a needle sharing drug den...).

As far as the effectiveness of the military, it isn't an open and shut case on whether they can control the epidemic, and as you rightly say if there are too few of them and the zombies are too effective then the zombies can still win. However, it doesn't take that many effective military personnel to contain the spread, and a full (although still a bit simplistic mathematical) analysis shows what the given thresholds are for a given zombie type.

[Junghalli]

Sooner or later, invincible zombies will get you no matter what you do.

Not necessarily, you just have to think in terms of containment instead of destruction. Lure them into traps and then entomb them in concrete, then store the blocks in some deep sturdy underground vault or something. Most movie zombies are stupid enough that this should be feasible.

Right now we are on the verge of armed protests because of fucking HEALTH CARE. Do you really think everyone's going to remain calm and do what the TV tells them to when they find out one of their horror-movie staples has come to life (relatively speaking) and is walking among them?

I think public fear will likely actually work in our favor here. Most people, when confronted with something really scary like the possibility of being eaten by zombies, are going to gravitate toward people who can protect them. Which means the people with lots of guns, i.e. the military.

I think we can make comparisons to real life disasters here. There's often some degree of social breakdown but generally as far as I can think of people in disaster areas don't start trying to actively oppose the people trying to help them.

[Simon_Jester]

Sooner or later, invincible zombies will get you no matter what you do.

Not necessarily, you just have to think in terms of containment instead of destruction. Lure them into traps and then entomb them in concrete, then store the blocks in some deep sturdy underground vault or something. Most movie zombies are stupid enough that this should be feasible.

Not in this model.

Invincible != invulnerable; invincible == "incapable of being overcome or defeated, inconquerable." An invulnerable zombie can be defeated as you describe: trap them in a place they cannot escape and you win. But an invincible zombie, by definition, cannot be defeated. And this model's zombies are invincible, because there is no way to permanently remove them from play. Disintegrate them and they go into "R" and eventually come back; drop them into a mineshaft and cover it over with ten feet of concrete and they go into "R"... and eventually come back.

For [gamma]>0, it's not a surprise that most of their starting conditions lead to the extinction of humanity.

Right now we are on the verge of armed protests because of fucking HEALTH CARE. Do you really think everyone's going to remain calm and do what the TV tells them to when they find out one of their horror-movie staples has come to life (relatively speaking) and is walking among them?

I think public fear will likely actually work in our favor here. Most people, when confronted with something really scary like the possibility of being eaten by zombies, are going to gravitate toward people who can protect them. Which means the people with lots of guns, i.e. the military.

I think we can make comparisons to real life disasters here. There's often some degree of social breakdown but generally as far as I can think of people in disaster areas don't start trying to actively oppose the people trying to help them.[/quote]

[Junghalli]

Not in this model.

Invincible != invulnerable; invincible == "incapable of being overcome or defeated, inconquerable." An invulnerable zombie can be defeated as you describe: trap them in a place they cannot escape and you win. But an invincible zombie, by definition, cannot be defeated. And this model's zombies are invincible, because there is no way to permanently remove them from play. Disintegrate them and they go into "R" and eventually come back; drop them into a mineshaft and cover it over with ten feet of concrete and they go into "R"... and eventually come back.

For [gamma]>0, it's not a surprise that most of their starting conditions lead to the extinction of humanity.

Well that's just a totally unrealistic assumption, even by zombie movie standards. Are they supposed to have teleport powers as well as total invulnerability? That's the only way I could imagine that this could work. Unless they're assuming that an immortal creature could dig its way out of any trap given sufficient time, which is I could see, but you could easily lock them up in things hard enough to get out of that the problem would be quite manageable. Bury them in concrete casks in a deep armored vault and we'd probably have the technology to launch them all into interstellar space or throw them into the sun (solving the problem permanently) long before there was a realistic possibility of them escaping.

[Simon_Jester]

Well that's just a totally unrealistic assumption, even by zombie movie standards. Are they supposed to have teleport powers as well as total invulnerability?

I think it's an unforeseen flaw in their model. They just don't have a category for "zombies put permanently out of action," only one for "beings put out of action." But since "beings put out of action" includes dead humans who will soon rise as zombies, there's a nonzero rate of transfer between "beings put out of action" and "active zombies." Any individual being put out of action eventually becomes an active zombie if you wait long enough under this model.

I don't think they intended to create invincible zombies that can never be permanently destroyed; they just underestimated the number of variables they'd need to create a good model of a zombie movie.

[Steel]

Well that's just a totally unrealistic assumption, even by zombie movie standards. Are they supposed to have teleport powers as well as total invulnerability?

I think it's an unforeseen flaw in their model. They just don't have a category for "zombies put permanently out of action," only one for "beings put out of action." But since "beings put out of action" includes dead humans who will soon rise as zombies, there's a nonzero rate of transfer between "beings put out of action" and "active zombies." Any individual being put out of action eventually becomes an active zombie if you wait long enough under this model.

I don't think they intended to create invincible zombies that can never be permanently destroyed; they just underestimated the number of variables they'd need to create a good model of a zombie movie.

I think that failing is a significant one as it results in Z+R being strictly increasing, and as the rate of transfer is k*R then the average length of time spent truly dead is only 1/k (due to the resulting exponential distribution). Thats why the only (vaguely) effective strategies were when they introduced the quarantine (as this didnt result in them wandering free again like, say, annihilation would) and when they introduced the "radical" measure of actually killing them!

[Simon_Jester]

Yes, that's exactly what I was getting at. I don't think they seriously intended to make zombies utterly unkillable on the assumption that this was a good model, but it does provide a baseline they can compare their other models to.

[Molyneux]

This does seem (disclaimer: I no be much good at the math) to be a decent model for the sillier zombie fare - say, "Pride & Prejudice & Zombies", where it is quite obvious (or at least never brought up) that there is no way of permanently putting down the unmentionable menace, only mitigating it.