## Chainsaw, Shotgun, Math. Which will you choose in the Zombie Apocalypse?

As an effect of the uprising in Zombie pop culture it is common to hear questions asked like “What weapon would you choose when the zombies take over the planet?” or “How would you stop the Zombie Apocalypse?”.  Now that those questions have become more popular than George A. Romero could have ever imagined, a new trend in answers to the age-old zombie apocalypse question is here.  Math.  Specifically, Game Theory, Calculus, and Linear Algebra.

Researchers at the University Of Ottawa have been studying Zombie outbreak strategy thoroughly and have recently published a research paper titled WHEN ZOMBIES ATTACK!: MATHEMATICAL MODELLING OF AN OUTBREAK OF ZOMBIE INFECTION.  This paper discusses the use of different scenarios involving zombies.  All scenarios assume elderly walking speed for zombies as in Night Of The Living Dead, that death from natural causes will also result in eventual “zombification”, the survivor birth rate is constant, and that a Zombies only payoff is living human brains.  By using these rules to modify existing mathematical models of infectious outbreak prediction they have come to a conclusion that may seem obvious. KILL ZOMBIES WHENEVER POSSIBLE. While this seems obvious it is actually the best strategy even when there is a treatment to make a zombie human again!  This is because those who have been treated are still susceptible.  The only way to truly remove a zombie from the graph theory model is to kill it through human-zombie interaction.  With the rate at which a human-zombie interaction can be successful undetermined, the best way to increase the amount of zombie kills is to increase the amount of zombie interactions.  As long as the interactions are chosen so that zombies are killed more often than humans, then mankind has some hope.  For more information, including the MATLAB code and flow charts that are very similar to the traffic network graphs we studied in class (except with each node representing either susceptible, removed, or zombie instead of City A, B, or C) check out the research paper.

Another intersection between math and the zombie apocalypse is a new game by Yahoo! Research labs called Shambling Hordes. The tagline is as follows:

Interested in game theory, advanced mathematics, classical economics and budget allocation problems? No? Let’s try again. Are you interested in commanding a legion of Zombie warriors in a pitched battle against your friends and random people online?

This game is similar to risk in that you move armies across territories on a map to capture the other player’s base, or in this case, tomb.  The difference here is that each player makes their move simultaneously.  When the two players confront each other on the same territory, they need to “battle”.  In battle, there are three strategies, left, right, and center.  Each player has 30 seconds to choose how many zombies will be placed in each section of the battlefield.  When the counter is up, the player with the more zombies in a section of the battlefield wins that section.  The player that wins the most section wins the battle.  This can be set up as an attack-defense graph.  Let’s say each player has 100 zombies.  If one player tried to split the zombies evenly among the sections, they would have to play it is 33, 33, 34 or some combination similar.  If the other player has a feeling that player 1 might do this, he can choose the strategy (35,35, 30).  This strategy wins two out of the 3 sections and thus the battle.  Be careful while playing though, it’s easy to focus on winning the battles and not the war.  Give it a shot and be the zombie king!