Zombie College: The 5 Rules of Lab Safety

What may be the best lab safety video ever.

Mutualism a.k.a Caterpillars Drugging Ants To Do Their Bidding

From the study - Figure 1. Attendant Workers of
Pristomyrmex punctatus standing on or around
Narathura japonica caterpillars

The manuscript is done! Submitted! Summer interns are finished. Boot up Normal Life Mode, please. Recommence blogging. So many good papers have come out during my hiatus. Where to start…where to start…

If you have read this blog for any amount of time then you will come across my fascination with ant manipulation, particularly zombification. This is why my cursor stopped over a new paper in Current Biology about caterpillars manipulating ants to do their bidding.

Let’s start with mutualism. This is a topic that I have visited in the past, and in ants for that matter. It’s a nice little relationship between species that involves an exchange of goods and/or services. In the natural world, this often means food and protection.

In this study, the researchers chose the Japanese oakblue butterfly (Narathura japonica), a lycaenid belonging to the Theclinae subfamily of butterflies. Many in this group are myrmecophilic, meaning they associate (often mutualistically) with ants in some way. The Japanese oakblue caterpillar has a specialized exocrine gland, the “dorsal nectary organ (DNO),” that is located on the seventh abdominal segment and is flanked by tentacle organs (TO). The DNO secretes sugar- and amino acid-rich honeydew while the TO secretes scents to “talk” to the ants. A “Come on down!” or “Danger, Will Robinson!” type thing. The ants tend to the caterpillars and keep them safe for a nice, sugary food reward. But is that all to the story? Obviously not or this post would end here.

To do this experiment, butterfly eggs and their associated ants (Pristomyrmex punctatus) were collected and reared separately. Then three test situations were set up with 50 ants per treatment:

1. “Experienced” ants – had free access to the caterpillars and their DNO secretions
2. “Inexperienced” ants – no caterpillar access, just some sugar soaked cotton balls
3. “Unrewarded” ants – had access only to caterpillars that had their DNO’s blocked (a little bit of clear nail polish goes a long way)

After 3 days in their test situation, 10 ants from each treatment were moved to Petri dishes that were set on pieces of white paper with a line on it to divide the dishes into 2 halves. After the ants acclimated to their new little plastic arenas, they were observed to see how many times they crossed the center line (“locomotory activity”). Also at the 3 day time point, ants and caterpillars were frozen in liquid nitrogen until their brains could be dissected out, specifically removing the optic lobes. Now, I’ve done some pretty small dissections, but those come nowhere close to ant brain removal! Wow, just wow. Once those itty bitty brains were out, they were processed for liquid chromatography-electrospray ionization-tandem mass spectrometry (LC-ESI-MS/MS) for serotonin, dopamine, octopamine, and tyramine. Very simply, that means making an ant-brain-aerosol that is then separated and identified by component.

They found that experienced ants had significantly less locomotory activity than the other two groups. So what does an ant walking, or in this case not walking, across a line even mean? Well, the fact that the ants are staying put signals that they are “standing guard” for the caterpillars. Okay, let’s say that standing means guarding, how do we know that this is really caterpillar-related and not just standing there? Well, first of all, it was only the experienced ants that did this. Second, the researchers observed that the caterpillars often “everted their TOs,” meaning that they turned them outward. This is typically a response the caterpillar makes when it is attacked by a predator – “Raise shields!” Experienced ants responded differently than the other two when they saw this caterpillar behavior in that they responded aggressively. This aggression is a response to the caterpillars’ alarm, one that has the ants defending against the predator. The fact that only experienced ants had these responses suggests that something in the DNO secretions is eliciting these defense behaviors.

So what is it about these secretions? That’s where the LC-MS/MS comes in. Biogenic amines are known function as neurotransmitters, neuromodulators, and/or neurohormones. This means that they can modify behavior in insects. DNO secretions contain biogenic amines. This analysis showed that experienced ant brains had low dopamine levels. Now, that’s important because dopamine has been shown to be involved in both locomotory activity and aggression in well studied organisms like fruit flies. Starting to see some links here, yes? To confirm the linkage, ants from each treatment were given reserpine, a small-molecule inhibitor that depletes dopamine but not serotonin in the brain. This test resulted the same behaviors, but the LC-MS/MS showed increased dopamine and serotonin in the ant brains. So same but different.

There is another aspect to consider: Who loses if the mutualism goes away? The honeydew is not the sole source of nourishment for the ants. They can leave and be still be fine. The caterpillar has much more to lose than the ant (its life via predation). So the caterpillars must be doing something besides sugar-loading their ants.  This is where the caterpillar gets sneaky - finding a way to make their ants to both stick around and defend against predators. As the authors put it, they they insert “manipulative drugs [into the honeydew] that could function to enforce cooperative behavior…from attendant ants.” Put that way, I’m okay calling it “ant mind control.”


Hojo, M., Pierce, N., & Tsuji, K. (2015). Lycaenid Caterpillar Secretions Manipulate Attendant Ant Behavior Current Biology DOI: 10.1016/j.cub.2015.07.016

p.s. The supplementary materials have a nice little video of ants in lined Petri dishes.

(image is Figure 1 from the above paper)

You've Got Red On You: Improving Z-Day Models

Yesterday I updated and expanded a long-ago post of mine called "Mmmm...Brains!: Using Mathematics To Save Us On Z-Day."This post summarized a book chapter in 2009 by Philip Munz, Ioan Hudea, Jo Imad, and Robert Smith? called "When Zombies Attack!: Mathematical Modeling of an Outbreak of Zombie Infection." This work was interesting because it combined basic biological assumptions and epidemic modeling with the rise and spread of zombies. Now, Caitlyn Witkowski of Bryant University and Brian Blais of Brown University have written a paper, which was published on the arXiv pre-print server, that extends the Munz et. al. (2009) work and then applies the methods to influenza dynamics.

Let's start with stochastic vs. deterministic models. Stochastic models are all about random variables and chance variations. They estimate probability distributions and outcomes by allowing for random variation over time, and they are good for small populations. Deterministic models assign individuals to subgroups or categories. They work well for large populations, assuming the size of each category can be calculated using only the history used to develop the model. This deterministic type of model is where we'll focus as it is heavily used in modeling disease dynamics. The categories used in a model each represent a specific stage of an epidemic with letters used in equations to represent each. The two types of disease models we'll focus on are the SIR model and the SEIR model. The SIR model is mathematically simpler and follows the flows of people between three states: susceptible (S), infected (I), and recovered/resistant (R). The SEIR model adds a fourth state, exposed (E), representing an infected individuals who are not yet symptomatic or infectious. This addition of a latency period is the primary difference between the models. Additional parameters are then added including the contact rate or transmission parameter (beta), removal of infection rate (alpha), rate from exposed to infected (sigma), rate of infected to recovered/resistant (gamma), and natural mortality rate (mu).

In order to create their model, Witkowski and Blas first needed data. As we currently have no data on actual zombies (that we know of), they gained insight into zombie dynamics by binge watching zombie films and television shows. From this they found that virtually all zombie movies fall into one of two forms that can each be represented by a particular film, either Night of the Living Dead (1968) or Shaun of the Dead (2004).

The Night of the Living Dead (which I'll abbreviate NotLD) category includes the following observations:

1. "Anyone who dies becomes a zombie, regardless of contact with one.
2. Because contact with a zombie is likely to lead to death, the interaction between the two subpopulations of susceptibles and zombies is signi cant.
3. This interaction between susceptibles and zombies results in a temporarily removed subpop- ulation before members of that population become zombies.
4. The only way in which a zombie can be permanently removed is by destroying the brain or burning the body."

The Shaun of the Dead (SotD) category's greatest difference from the NotLD is that contact between a susceptible and a zombie is necessary for the zombie population to grow. Not all susceptibles who die become zombies.

With this knowledge, they used the SIR-type models and applied Bayesian parameter estimations. They then applied Markov Chain Monte Carlo (MCMC) techniques to estimate the posterior probabilities of the parameters. This allowed them to provide both the best estimates and their uncertainty. In both movie categories, they were able to estimate the initial susceptible population by using simple approximation, estimated zombie numbers from scenes with a field of view approximately 50 meter squared area, and estimate overall time values from visual cues (clocks, sun, etc.). They then used the exact same techniques to analyze real-world data on influenza using Google Trend data.

Witkowski and Blas found their models to be a significant improvement over the models in Munz et. al. (2009) in that their model structure had a closer match to the zombie system. They found that when they removed Munz et. al.'s "recycling" parameter (humans in the removed class can resurrect and become a zombie) the stability of the system changed significantly. This showed that the zombies can be completely removed as long as they are removed faster than they are created. They found the rates of infection and removal (beta and alpha, respectively) to be nearly a factor of two smaller for SotD than for NotLD. NotLD also has a higher value for the rate of exposed becoming fully infected than does SotD. NotLD also shows an interesting joint distribution patterns in that higher values of the infection rate (beta) require a higher rate of removal of infection (alpha), and no relationship between the removal rate of infection and the rate of exposed becoming fully infected (sigma).  In both the NotLD and the SotD categories military intervention saves human civilization, the strength of this military attack and time at which it occurs being the two major factors determining the success. A quick, early intervention expectedly annihilates the zombie horde, but a later intervention is essentially a wasted effort. They explored this scenario with SotD. They assumed that the military intervention seen at the end of the film increased the alpha parameter ten-fold which effectively eliminates the zombies, restoring civilization. However, their calculations suggest that if the film had lasted 30 minutes longer, the same intervention strength would have lead to a doomsday scenario. So this model does agree with Munz et. al. that timing is everything.


Caitlyn Witkowski, & Brian Blais (2013). Bayesian Analysis of Epidemics - Zombies, Infuenza, and other Diseases arXiv.org, 1-16
https://arxiv.org/pdf/1311.6376

Learn more about SIR-type disease models:

Murali Haran's presentation slides "An introduction to models for disease dynamics"
Hans Nesse's description and simulator his page "Global Health - SEIR Model"
Jeffrey Moehlis tutorial page "An SEIR model"
Ottar Bjørnstad's 2005 paper "SEIR models"

Some other blog write-ups:

Geekosystem's article "Mathematicians Wrote a Paper on How the Zombie Apocalypse Won’t Kill Us All, Made Us Grateful for Math"
Medium's article "Mathematical Model of Zombie Epidemics Reveals Two Types of Living-Dead Infections"


(image via IMDB)

Castrating the Zombie Ant

Last year I posted Attack of the Zombie Ant! A post that turned out to be quite popular. To sum it up, there are fungal parasites (genus Ophiocordyceps) that infect ants and take control of their bodies. The fungus then compels the ant to crawl up into the forest canopy and clamp down on a leaf while the fungus grows inside the body, eventually producing a hyphae and stroma (fruiting body) that grows out of the head and produces and releases spores. And repeat.

A recent paper in PLoS ONE takes a closer look the coevolution between ant colonies and these rare, specialized fungi. Broadly, the term coevolution is used to describe how two or more species reciprocally affect each other's evolution. In the case of the zombie ants, it is host-parasite coevolution. The parasite evolves to infect the host, and the host evolves to resistant to the parasite. An arms race, if you will. The virulence and defense traits of specialized parasites, such as the zombie-ant fungi, are shaped by these arms races. This is even more true in species like Ophiocordyceps that rely on host behavior for their reproductive success. On the other side of the coevolutionary coin, ant colonies (in this case Formica and Camponotus ants) are long-lived and live in high density, continuously interacting colonies. This behavior has been shown to be a type of social immunity where there is a strong selection for efficient prophylactic defenses and where ant parasites pose a limited threat to infecting an entire colony. Meaning that individual ants my die from the fungal disease but that the mortality of the colony is low.

This paper specifically looks at the trade-offs experienced by Ophicordyceps manipulating ants into dying in nearby graveyards. When the fungus compels an ant to leave their nest and die close to their host colony, many infected individuals will end up in one area, forming high-density ant graveyards that may persist for years. Considering the life span of your average ant, that is a long time. The authors of this paper used data from previous studies of O. unilateralis in Thailand and collected a new data set from O. camponoti-rufipedis from Brazil to construct a developmental-stage-structured model describing this ant-fungus interaction. In this new collection, they identified ants infected with O. camponoti-rufipedis and marked areas covering entire graveyards, tagging all dead infected ants. Each cadaver ant was then characterized in terms of parasite development: (1) freshly killed ant, (2) dead ant with parasite stroma, (3) dead ant with mature fruiting body, (4) dead ant at stage 2 or 3, but hyperparasitized by other fungi, or (5) dead ant whose status could not be identified. To estimate the infectivity of the fungi's fruiting bodies, they collected a sample of dead ants and brought them to the lab for study. From these data, they were able to formalize the "life-cycle" of parasitized ants and calculate a growth rates and fungal developmental stage distributions of the graveyards.

The researchers found that only 6.5 percent of the O. camponoti-rufipedis fruiting bodies were effectively producing spores. Most of the dead ants that they found were sterile because they were either immature, damaged or hyperparasitized (secondarily parasite develops within a previously existing parasite). They also found that only 42 percent of the fruiting bodies were shooting spores at a particular time interval. When the apparently "healthy" cadaver ants were dissected, they found them to have been invaded by the larvae of small unidentified arthropods which may have reduced the likelihood of the fungi reaching maturity. Add to this that out of all of the ant colony members, only the foragers face the risk of encountering spores, then you end up seeing a rather low infection and transmission rate. So only if graveyards are stable or growing will infection levels be stable.

Interestingly, the authors found that the zombie-ant fungi are themselves vulnerable to attack by other parasites. Their model suggests that the stroma life stages or immature fruiting body stages are highly vulnerable to biotic attack. So much so that hyperparasitism is nearly negligible in the mature life stage. Whether that is because the mature life stage has a much more efficient immune defense or some other cause is unclear. What is clear is that hyperparasitic fungi prevent the infected zombie-ant fungus from spreading spores which, in turn, means that fewer of the ants will become zombies. This means that the rate of infections is much less than the size of some graveyards might suggest. It is known that O. unilateralis has a range of asexual stages (synanamorphs) with spores adapted for persistence or aerial dispersal. However, O. camponoti-rufipedis is known to produce a single anamorph. So the horizonatal transmission of this species may depend on the movement of the infected ants themselves. And that means all kinds of other intriguing studies may be in the works. Can't wait!


Sandra B. Andersen, Matthew Ferrari, Harry C. Evans, Simon L. Elliot, Jacobus J. Boomsma, & David P. Hughes (2012). Disease Dynamics in a Specialized Parasite of Ant Societies PLoS ONE, 7 (5) DOI: 10.1371/journal.pone.0036352


About the Authors:
Sandra Andersen's bio
David Hughes' Lab (includes zombie-ant videos on his Projects page)

Articles:
Penn State Science "The Zombie-Ant Fungus Is Under Attack, Research Reveals"
Discover Magazine "Zombie Ant Parasite Has Its Own Parasite - a Fungus that Attacks Fungi"
The Guardian "Zombie-ant parasitic fungus kept in check by hyperparasitic fungus"


(image from the Hughes Lab website)

The Science of Surviving Z-Day

I'm not sure why so many zombie survival guides are coming out lately. Perhaps it is due to their popularity in pop culture, or maybe just because we find them fascinating in a creeped-out kind of way. Regardless, I see little finds like this one as entertaining. I found this "The Science of Surviving the Zombie Apocalypse" over on the 2dayBlog, and as it is science related (if very tangentially so), informative (if it so applies), and funny (not so tangentially so) I decided to share it with you. Enjoy!

Click image for a large view

Like this, then take a look at this Flowchart: How Long Would You Survive a Campus-Wide Zombie Outbreak via CollegeHumor

Z-Day: Are You Prepared?

I was catching up on some NPR Wait Wait Don't Tell Me and heard about this story. The Centers for Disease Control and Prevention (CDC) has released a new emergency guide on their Preparedness and Response webpage and in their Public Health Matters Blog. The guide is called Social Media: Preparedness 101: Zombie Apocalypse. The idea here being that if you are prepared for a zombie apocalypse then you are prepared for any emergency. Genius.

After a brief history of zombies the entry goes into general safety for when zombies (or hurricanes, pandemics, etc.) rise up. First, have an emergency kit in the house containing water (1 gal per person per day), food (non-perishables), medications, tools and supplies (utility knife, duct tape, battery powered radio, etc.), sanitation and hygiene products (bleach, soap, towels, etc.), clothing and bedding, important documents (driver's license, passport, birth certificate, etc.), and first aid supplies. Although, with that last one, you're a goner if a zombie bites you, but if you, let's say, cut yourself while boarding up your house against zombies then you'll be all set. Next, you should have an emergency plan. Identify all of the types of emergencies possible, besides and/or including zombie attacks. Know where to go and who to call when the zombies start lumbering down your street. Pick a rendezvous point (one close, one far) and identify emergency contacts. Plan your evacuation route. Despite being mostly brain dead, zombies are rather clever and definitely relentless when going after prey (you) and so you should not only know where to go but multiple, safe ways to get there. And finally, the CDC ends their post with a plea (well, I'm calling it a plea) for you to trust them to track the outbreak of the zombie infection and provide assistance. That is if they are not all zombies themselves.

Now that we're prepared how do we go about realistically (yeah, someones modeled it!)getting rid of the zombie plague? Go back to the short but informative Mmm...Brains! post from April of last year to find out.

Read the entire entry here:
http://www.bt.cdc.gov/socialmedia/zombies_blog.asp and http://blogs.cdc.gov/publichealthmatters/2011/05/preparedness-101-zombie-apocalypse/
and grab your own buttons, badges and widgets here: http://emergency.cdc.gov/socialmedia/zombies.asp

Also...
http://www.latimes.com/health/boostershots/la-heb-cdc-zombie-apocalypse-20110519,0,6704265.story
http://www.cnn.com/2011/HEALTH/05/19/zombie.warning/index.html
http://www.naturalnews.com/032454_zombie_apocalypse_CDC.html
http://www.npr.org/templates/story/story.php?storyId=136500576

Attack of the Zombie Ant!

A couple of years ago a study was published in The American Naturalist about an interesting fungal parasite known as Ophiocordyceps unilateralis. This fungus infects ants in the tribe Camponotini (carpenter ants) but does not kill them outright. Rather, the ant remains alive for a short time but the fungus is in control. The fungus compels the ant to crawl down from its nest in the high forest canopy down to the small plants of the understory. Then the fungus has the ant crawl onto the underside of a leaf, clamp down its mandibles, and then die. There the ant body will stay while the fungus continues to grow inside of its body, producing a hyphae and stroma (fruiting body) that grows right out of the ant's head. The stroma then releases spores on to the forest floor, spores waiting to infect the next unsuspecting ant passerby. You can see where the nickname "zombie ants" and "zombie fungus" came from. Now, this was not a previously unknown species of fungus but rather an unknown effect of the fungus on ants, a previously unknown part of the life cycle. What is truly amazing is the accuracy to which the fungus directed the ant. The ants always clamped on to the underside of a leaf and almost always on a leaf vein. The chosen leaf was about 25 centimeters above the ground, with 94-95% humidity, and between 20-30 Celsius. The fungus directs the ant to a location with the parameters that it needs to survive and reproduce.

Now a new paper in the journal PLoS ONE describes four new species belonging to the O. unilateralis species complex from the Atlantic rainforest in Brazil. The species are named according to their ant host species (specifically Camponotus rufies, C. balzani, C. melanoticus, and C. novograndadensis). Ultimately, this paper is just recognizing and naming new species. However, it helps to draw attention to the south-eastern region (Zona de Mata) of the State of Minas Gerais in Brazil, one of the most heavily degraded biodiversity hotspot on the planet. A total of 92% of this rainforest is gone, and four new species have just been discovered. How many more are there to find and how many have already been lost?

Want more zombie animals? Check out these:
The nematode-ant relationship in Central America
The emerald cockroach wasp (Ampulex compressa)-cockroach relationship in the Polynesian Islands.
The spider (Plesiometa argyra)-wasp (Hymenoepimecis argyraphaga) relationship in Costa Rica.

The list goes on and on; pill bugs and spiny-headed worms (Plagiorhychun cylin-draceus), grasshoppers (Melanoplus sanguinipes) and the protist (Nosema acridophagus), the fluke (Dicrocoelium dendriticum) and the ant, the wasp (Glyptapanteles) and the caterpillar, the distome (Leucochloridium paradoxum) and the snail, the barnacle (Sacculina carcini) and the crab, etc. Wasps, ants, and caterpillars tend to have a lot of parasite-host stuff going on (there's even a whole group of parasitoid wasps), although admittedly not all that much zombism. It is an ever-so-interesting evolutionary arms race!

Read more about zombie animals here: http://www.newscientist.com/article/mg14018983.500-evolutions-neglected-superstars-there-is-nothing-glamorous-about-fleas-flukes-or-intestinal-worms-so-why-are-they-suddenly-attracting-so-much-attention.html
and here: http://discovermagazine.com/photos/04-zombie-animals-and-the-parasites-that-control-them

The original zombie ant study (online version of the paper contains a video):
Andersen, Sandra B., et al. (2009) The Life of a Dead Ant: The Expression of an Adaptive Extended Phenotype. The American Naturalist: 174(3), 424-433. (DOI: 10.1086/603640)

The new study, and because it is published in PLoS ONE it is free access (yay!):
Evans, Harry C., Simon L. Elliot, and David P. Hughes. (2011) Hidden Diversity Behind the Zombie-Ant Fungus Ophiocordyceps unilateralis: Four New Species Described from Carpenter Ants in Minas Gerais, Brazil. PLoS ONE: 6(3), e17024. (DOI:10.1371/journal.pone.0017024)

Online stories on this paper:
http://blogs.plos.org/everyone/2011/03/02/four-new-species-of-zombie-ant-fungi-another-step-forward-for-open-access-taxonomy/%20
http://www.physorg.com/news/2011-03-species-zombie-ant-fungi-brazilian.html
http://www.sciencedaily.com/releases/2011/03/110302171309.htm

Mmmm...Brains!: Using Mathematics To Save Us On Z-Day

Updated and Expanded: 1-14-2014

In the science of the undead it's publish or perish, and rise to publish again. Make no mistake, the threat of zombies is real and Z-day is closer than you think. If caught unprepared you may wake up with a flesh-hungry, reanimated corpse on your doorstep.

But, realistically, can we use what we already know to examine a zombie outbreak?

Philip Munz, Ioan Hudea, Jo Imad, and Robert Smith? (yes, there really is a question mark in his name) wrote a book chapter in 2009 called "When Zombies Attack!: Mathematical Modeling of an Outbreak of Zombie Infection."  This article models a zombie attack, using basic biological assumptions and equations currently used to examine the spread of infections such as HIV, malaria, and HPV. It also takes into account what we know (or think we know) about zombies: they are cannibalistic, they move in small, irregular steps (using the popular slow-zombie rather than the newer fast-zombie), they show signs of physical decomposition, and their bite changes a non-zombie into a zombie.

Munz et al.'s basic model considered three basic classes: susceptible, zombie, and removed. Susceptibles become deceased through natural, non-zombie-related causes but can become zombies through bite/blood transmission. As it suggests, the removed are those who have died via attack or natural causes. So, assuming a short time period where the birth rate is constant, zombies can only come from the resurrected or susceptibles, and zombies move to the removed class when they are defeated. Using these variables he was able to put together a simple model. Then things got more complicated, as models tend to do.

The authors took his basic model and ran it through different scenarios, adding parameters as needed. The first factors he looked at were mass-action incidence and random contact. These basic additions show a disease-free equilibrium to be unstable and a human-zombie coexistence to be impossible. Next, they revised the model to include a latent class of infected individuals which shows that although the zombies will still take over, it will take approximately twice as long. The next version of the model was run with a partial quarantine of zombies then there will be a slight delay in the time to eradication but, ultimately, the zombies still get us. Then the model was run assuming a cure has been found that allows a zombie to return to human form but does not offer immunity. In this case, humans are not eradicated, but only exist in low numbers. Better but still not great. Finally, they attempted to control the zombie population by strategically destroying them as Max Brooks suggests in his book World War Z - An Oral History of the Zombie War. This scenario assumes that it would be difficult to have the resources and coordination needed and so more than one attack would be needed resulting in an impulsive effect. This model found that after 2.5 days, 25 percent of the zombies destroyed; after 5 days, 50 percent; after 7.5 days, 75 percent; and after 10 days, 100 percent of zombies were destroyed. It is important to note that the time scale of this model is short. If the time scale of the outbreak increases then you get a doomsday scenario with a complete collapse of civilization, every human infected or dead. Essentially, if we can contain the outbreak initially and quickly then we can save our own asses (literally).

Next, consider Daniel Lakeland's Improved Zombie Dynamics model over at his Models of Reality blog. He builds on the above model, taking into account several factors that Smith?'s group did not include. Lakeland's model removes the short timescale, allowing the human population to grow at approximately 4.5 percent per year growth through a birth rate of 6.5 percent and a death rate of 2 percent. He also tackles the classification categories. Once a zombie is categorized as removed it can not be reanimated and therefore a special class of fully removed zombies should be required. Also in this fully removed category should go those human who died of natural causes too long ago to be zombified (basically, skeletons). Resurrection from the dead is assumed to be a relatively rare event, 1 percent per year, and rotting of the dead to be much faster, perhaps 5 percent per day. Any good model should also take human experience into account. Surviving humans have learned how to fight zombies and avoid zombification.  Initially, the probability of a human winning a zombie fight is relatively low, about 0.1 percent, but then again the percentage of zombies starts out low too, about 1 in 10,000. But the zombie-killing learning parameter is quite large. Elite zombie killers, in particular, serve an important role in that they are most efficient, rapid, and effective in zombie eradication. However, this skill decays at approximately 1 percent per day in the absence of education. The lack of skill and readiness makes all the difference and causes the probability of a human victory to decline rapidly to zero. It is this, the education parameter, that Lakeland's model found to be most important. Reasonably large numbers of people should be at the very least vigilant with an elite force (perhaps 4/10,000 people) there to drop some zombies. So watch some zombie movies, ya'll.

Philip Munz, Ioan Hudea, Joe Imad, & Robert J. Smith? (2009). When zombies attack!: Mathematical modelling of an outbreak of zombie infection Infectious Disease Modelling Research Progress, 133-150
http://www.staff.science.uu.nl/~frank011/Classes/modsim/Handouts/Zombies.pdf

Lakeland, D. (2010). Improved zombie dynamics. Models of Reality blog, 1 March.
http://models.street-artists.org/?p=554

Robert Smith?'s articles:
"A report on the zombie outbreak of 2009: how mathematics can save us (no, really)"
"What can Zombies Teach us about Mathematics?"

NPR interview with Robert Smith?: "Who Will Win In Human, Zombie War?"
CBC News Story: "Zombie Math"

Some other things to consider:

This unpublished paper by Andrew Gelman on a way to study zombies indirectly using surveys that don't risk the interviewers: "'How many zombies do you know?' Using indirect survey methods to measure alien attacks and outbreaks of the undead"

Blake Messer over at The Tortoise's Lens blog creates a model where looks at the Munz model and he takes into account that the humans who survive do so for a reason (they are stronger, faster, smarter, etc.) and the distribution of these people in a two dimensional landscape. Read his post called "Agent-Based Computational Model of Humanity's Prospects for Post Zombie Outbreak Survival"

(image from www.disastertaskforce.com)