Math Protects You Against Zombies

 

It's amazing how zombies took over the imagination of people in the movies, television, books, and even in music.  People love watching the fight between humans and zombies.  The fascination with zombies has reached the point where math has been used to explain how to survive a zombie apocalypse. 

We've seen articles covering this topic but from a survivalist point of view rather than a mathematical view.  Numberphile on Youtube created a video explaining the math of zombies using the diffusion equation.  

We know that zombies tend to move around randomly while diffusing through a population.  In addition, there are three possible outcomes to the scenario.  First is the zombie kills the person, the person kills the zombie, or the zombie infects the human, making another zombie.  So the person giving the explanation ends up using partial differential equations to determine the best course of action to survive the encounter. 

One conclusion based on the relationship between distance and time is that one should run away rather than staying to fight. In fact, the object is to kill zombies faster than zombies are being made. This is because zombies invade at a rate proportional to their speed and distance from us.  Earlier predictions said the Rocky Mountains is a great place to retreat to but any real rural area away from cities would be good since it would take a while for zombies to get through the population before heading out.

Back in 2017, a study conducted by students at the University of Leicester and published in the Journal of Physics Special Topics determined that within 100 days of "ground zero", the number of zombies would radically outnumber the uninfected. The study based it's math on the premise of one zombie converting one person each day. The conclusion stated with a 90% certainty, there would be only 273 survivors left after 100 days.  They used the SIR model which is a model used to calculate the spread of disease within a population.  The students included the idea that over time, the survivors are less likely to become infected due to learning to fight better, In a follow up study when they included human reproductive rates with better rates of killing zombies, it was determined that over time, humans would win out over zombies. 

In another study done by PhD students at the University of Sheffield explored the question of what happens if people choose to stay and fight the zombies.  These students also used the SIR model to answer the question.  They determined that more people would come back as zombies if they stayed and fought the zombies.  These students also ran the numbers for the scenario of sending in the military to fight but the result came back about the same. In their testing different scenarios, hiding from the zombies came back as a decent choice as long as they were not found.  If they were found, they would end up infected.  The premier solution would be to domesticate the zombies.  

In the first situation, the person looked at the math of spread using partial differential equations while in the other two studies, students relied on the same mathematical modeling used to determine the spread of disease in humans and in nature and what happens when a vaccination is used which is equivalent to the domestication of zombies in the zombie apocalypse.  So mathematics applied in two different ways based on whether it is a disease or something that is diffused.  Let me know what you think, I'd love to hear.  Have a great day.